Relative order and type of entire functions represented by Banach valued Dirichlet series in two variables
Dibyendu
Banerjee
Department of Mathematics, Visva-Bharati, Santiniketan- 731235, India
author
Nilkanta
Mondal
Ballavpur R.G.S.Vidyapith, Ballavpur-713323, Raniganj, India
author
text
article
2016
eng
In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of its partial derivative.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
1
14
https://ijnaa.semnan.ac.ir/article_288_5d4b6ff0b04ebc85198867c84f85d85c.pdf
dx.doi.org/10.22075/ijnaa.2016.288
On the quadratic support of strongly convex functions
S.
Abbaszadeh
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, Iran
author
M
Eshaghi Gordji
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, Iran
author
text
article
2015
eng
In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2015
15
20
https://ijnaa.semnan.ac.ir/article_273_368395c1469c8c8c42fa81b1d2a2a883.pdf
dx.doi.org/10.22075/ijnaa.2015.273
Nonexpansive mappings on complex C*-algebras and their fixed points
Davood
Alimohammadi
Department of Mathematics, Faculty of Science, Arak university, Arak 38156-8-8349, Iran
author
text
article
2015
eng
A normed space $\mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E \longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $\mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (iii) $C_0 (X)$ does not have the fixed point property. We also show that if $A$ is a commutative complex $\mathsf{C}^*$-algebra with nonempty carrier space, then the following statements are equivalent: (i) Carrier space of $ A $ is infinite, (ii) $ A $ is infinite dimensional, (iii) $ A $ does not have the fixed point property. Moreover, we show that if $ A $ is an infinite complex $\mathsf{C}^*$-algebra (not necessarily commutative), then $ A $ does not have the fixed point property.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2015
21
29
https://ijnaa.semnan.ac.ir/article_289_75ca5b7bd96a777bf6f51352b152a680.pdf
dx.doi.org/10.22075/ijnaa.2015.289
On the fine spectrum of generalized upper triangular double-band matrices $\Delta^{uv}$ over the sequence spaces $c_o$ and $c$
Javad
Fathi
Department of Mathematic, Faculty of Science, Hormozgan University, Bandarabbas, Iran
author
text
article
2016
eng
The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices $\Delta^{uv}$ over the sequence spaces $c_o$ and $c$. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun [V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics, 234(2010) 1387-1394].
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
31
43
https://ijnaa.semnan.ac.ir/article_290_35d0cd244cf09dff6eaf8a53cd56341d.pdf
dx.doi.org/10.22075/ijnaa.2015.290
Common fixed point theorem for nonexpansive type single valued mappings
Pankaj
Jhade
NRI Institute of Information Science & Technology, Bhopal, MP, 462021, India
author
A. S.
Saluja
J H Govt. PG College, Betul, 460001, India
author
text
article
2016
eng
The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of nonexpansive type multivalued and single valued maps, European J. Pure Appl. Math., 4 (2011) 330-339].
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
45
51
https://ijnaa.semnan.ac.ir/article_293_565f06624c411fcd198bd19c2a9d1e4a.pdf
dx.doi.org/10.22075/ijnaa.2015.293
Some fixed point theorems for weakly subsequentially continuous and compatible of type (E) mappings with an application
Said
Beloul
Department of Mathematics and Informatics, Faculty of Sciences and Technology, University of Eloued, P.O.Box 789,
Eloued 39000, Algeria
author
text
article
2016
eng
In this paper, we will establish some fixed point results for two pairs of self mappings satisfying generalized contractive condition by using a new concept as weak subsequential continuity with compatibility of type (E) in metric spaces, as an application the existence of unique common solution for a system of functional equations arising in system programming is proved.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
53
62
https://ijnaa.semnan.ac.ir/article_294_616d183be61dda4a9cc57edf91853d69.pdf
dx.doi.org/10.22075/ijnaa.2015.294
Approximate a quadratic mapping in multi-Banach spaces, a fixed point approach
Sattar
Alizadeh
Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran
author
Fridoun
Moradlou
Department of Mathematics, Sahand University of Technology, Tabriz, Iran
author
text
article
2016
eng
Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:\begin{equation}\sum_{ j = 1}^{n}f\Big(-2 x_{j} + \sum_{ i = 1, \neq j}^{n} x_{i}\Big) =(n-6) f\Big(\sum_{ i = 1}^{n} x_{i}\Big) + 9 \sum_{ i = 1}^{n}f(x_{i}).\end{equation}
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
63
75
https://ijnaa.semnan.ac.ir/article_295_c27b0b230605db7769e5251a845fed26.pdf
dx.doi.org/10.22075/ijnaa.2015.295
On the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications
Huseyin
Budak
Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey
author
Mehmet
Sarikaya
Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey
author
text
article
2016
eng
In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
77
85
https://ijnaa.semnan.ac.ir/article_296_24c7771b70f4d911a2cd1e8f6b47c36b.pdf
dx.doi.org/10.22075/ijnaa.2015.296
Generalized solution of Sine-Gordon equation
Lalla Saadia
Chadli
Laboratoire de Mathematiques Appliquees & Calcul Ssientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni
Mellal, Morocco
author
Said
Melliani
Laboratoire de Mathematiques Appliquees & Calcul Ssientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni
Mellal, Morocco
author
Abdelaziz
Moujahid
Laboratoire de Mathematiques Appliquees & Calcul Ssientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni
Mellal, Morocco
author
Mhamed
Elomari
Laboratoire de Mathematiques Appliquees & Calcul Ssientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni
Mellal, Morocco
author
text
article
2016
eng
In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
87
92
https://ijnaa.semnan.ac.ir/article_297_7593898e083c1954e8404529bfff0844.pdf
dx.doi.org/10.22075/ijnaa.2015.297
Titchmarsh theorem for Jacobi Dini-Lipshitz functions
Mustapha
Boujeddaine
Department of Mathematics and Computer Sciences, Faculty of Sciences, Equipe d Analyse Harmonique et Probabilies, Universite Moulay Ismail,
BP 11201 Zitoune, Meknes, Morocco
author
Said
Fahlaoui
Department of Mathematics and Computer Sciences, Faculty of Sciences, Equipe d Analyse Harmonique et Probabilies, Universite Moulay Ismail,
BP 11201 Zitoune, Meknes, Morocco
author
Radouan
Daher
Department of Mathematics, Faculty of Sciences An Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, Morocco
author
text
article
2016
eng
Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $\mathrm{L}_{(\alpha,\beta)}^{p}(\mathbb{R}^{+})$, $(1< p\leq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lipschitz condition in $L^{p}$.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
93
101
https://ijnaa.semnan.ac.ir/article_298_98bc5a10d20c0d2f6d2e2df1b9b479f4.pdf
dx.doi.org/10.22075/ijnaa.2015.298
Some new results using Hadamard fractional integral
Sabrina
Taf
Department of Mathematic, Faculty SEI, UMAB University of Mostaganem, Algeria
author
Kamel
Brahim
Faculty of science of Tunis, Tunisia
author
text
article
2015
eng
Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse Minkowski's type are obtained for positive functions resulting in two theorems.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2015
103
109
https://ijnaa.semnan.ac.ir/article_299_8f090a9047f90a63156afc736973f47f.pdf
dx.doi.org/10.22075/ijnaa.2015.299
Some common fixed point theorems for four $(\psi,\varphi)$-weakly contractive mappings satisfying rational expressions in ordered partial metric spaces
R.A.
Rashwan
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
author
S.M.
Saleh
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
author
text
article
2015
eng
The aim of this paper is to prove some common fixed point theorems for four mappings satisfying $(\psi,\varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2015
111
130
https://ijnaa.semnan.ac.ir/article_300_ee2c2f17e0cefae6067c770ab7ee52a6.pdf
dx.doi.org/10.22075/ijnaa.2015.300
A determinant inequality and log-majorisation for operators
Seyed Mahmoud
Manjegani
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111
author
text
article
2016
eng
Let $\lambda_1,\dots,\lambda_n$ be positive real numbers such that $\sum_{k=1}^n \lambda_k=1$. In this paper, we prove that for any positive operators $a_1,a_2,\ldots, a_n$ in semifinite von Neumann algebra $M$ with faithful normal trace that $\t(1)<\infty$, $$\prod_{k=1}^n(\det a_k)^{\lambda_k}\,\le\,\det (\sum_{k=1}^n \lambda_k a_k),$$where $\det a=exp(\int_0^{\t(1)} \mu_a(t)\,dt)$. If furthermore $\t(a_i)<\infty$ for every $1\le i\le n$ and $ \prod_{k=1}^n(\det a_k)^{\lambda_k}\neq 0$, then equality holds if and only if $a_1=a_2=\cdots =a_n$. A log-majorisation version of Young inequality are given as well.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
131
140
https://ijnaa.semnan.ac.ir/article_301_f16f986333a145f2dd7a7128e1029da9.pdf
dx.doi.org/10.22075/ijnaa.2015.301
On the $s^{th}$ derivative of a polynomial
Abdullah
Mir
Department of Mathematics, University of Kashmir, Srinagar, $190006$, (India)
author
text
article
2015
eng
For every $1\leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2015
141
145
https://ijnaa.semnan.ac.ir/article_130_55c76fca4b5e4d033c72d893fe0a47b7.pdf
dx.doi.org/10.22075/ijnaa.2015.130
Vector ultrametric spaces and a fixed point theorem for correspondences
Kourosh
Nourouzi
Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
author
text
article
2016
eng
In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
147
153
https://ijnaa.semnan.ac.ir/article_302_8a23d5e13714c2c3f04be5ce3ed78c8c.pdf
dx.doi.org/10.22075/ijnaa.2015.302
Variational inequalities on Hilbert $C^*$-modules
Hedayat
Fathi
Department of Mathematics, Shahid Beheshti University, Tehran, Iran
author
S.A.R.
Hosseinioun
Department of Mathematics, Shahid Beheshti University, Tehran, Iran;
Department of Mathematics, University of Arkansas,
Fayetteville, Arkansas 72701, USA
author
text
article
2015
eng
We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory on Hilbert $C^*$-modules is studied.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2015
155
165
https://ijnaa.semnan.ac.ir/article_303_379b7e5db0cd9d58ab8583a7f784939c.pdf
dx.doi.org/10.22075/ijnaa.2015.303
Approximately generalized additive functions in several variables via fixed point method
R.
Farokhzad Rostami
Department of Mathematics, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran
author
S.A.R.
Hoseinioun
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA
author
text
article
2016
eng
In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equation\begin{align*}&D_f(x_{1},.., x_{m}):= \sum^{m}_{k=2}(\sum^{k}_{i_{1}=2}\sum^{k+1}_{i_{2}=i_{1}+1}... \sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(\sum^{m}_{i=1, i\neq i_{1},...,i_{m-k+1} } x_{i}-\sum^{m-k+1}_{ r=1} x_{i_{r}})\\& \hspace {2.8cm}+f(\sum^{m}_{ i=1} x_{i})-2^{m-1} f(x_{1})=0\end{align*}where $m \geq 2$ is an integer number.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
167
181
https://ijnaa.semnan.ac.ir/article_304_9d50c3cecad33f485b18a635d7221af3.pdf
dx.doi.org/10.22075/ijnaa.2015.304
Coupled coincidence point in ordered cone metric spaces with examples in game theory
Alireza
Naeimi Sadigh
Department of Mathematics, Statistics and Computer science, Semnan University, P.O. Box 35195-363, Semnan, Iran
author
Samaneh
Ghods
Department of Mathematics, Islamic Azad University, Semnan Branch, Semnan, Iran
author
text
article
2016
eng
In this paper, we prove some coupled coincidence point theorems for mappings with the mixed monotone property and obtain the uniqueness of this coincidence point. Then we providing useful examples in Nash equilibrium.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
183
194
https://ijnaa.semnan.ac.ir/article_305_50df6bdc73b5dc783d4dfd0d2c6a6513.pdf
dx.doi.org/10.22075/ijnaa.2015.305
On a class of paracontact Riemannian manifold
Mahmood
Parchetalab
Department of Mathematics, Faculty of Science, Arak university, Arak 38156-8-8349, Iran
author
text
article
2016
eng
We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
195
205
https://ijnaa.semnan.ac.ir/article_306_7b5dec458ce15e057e2a3d1addca1f0b.pdf
dx.doi.org/10.22075/ijnaa.2015.306
Existence of solution and solving the integro-differential equations system by the multi-wavelet Petrov-Galerkin method
Mohsen
Rabbani
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
author
text
article
2016
eng
In this paper, we discuss about existence of solution for integro-differential system and then we solve it by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in the process of discretizing and we drive a system of algebraic equations with small dimension which it leads to approximate solution with high accuracy. We compare the results with similar works and it guarantees the validity and applicability of this method.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
207
218
https://ijnaa.semnan.ac.ir/article_307_74c3fcefd0d66fde79c657652f29cbcd.pdf
dx.doi.org/10.22075/ijnaa.2015.307
On fixed points of fundamentally nonexpansive mappings in Banach spaces
Mohammad
Moosaei
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
author
text
article
2016
eng
We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
219
224
https://ijnaa.semnan.ac.ir/article_308_db07694ccc7a387cc590bac3f64bd749.pdf
dx.doi.org/10.22075/ijnaa.2015.308
Common fixed point of multivalued graph contraction in metric spaces
Masoud
Hadian Dehkordi
Department of Mathematics, Faculty
of Basic Science,Iran University of Science and Technology, Narmak, Tehran,Iran
author
Masoud
Ghods
Department of Mathematics, Faculty
of Basic Science,Iran University of Science and Technology, Narmak, Tehran,Iran
author
text
article
2016
eng
In this paper, we introduce the (G-$\psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
225
230
https://ijnaa.semnan.ac.ir/article_309_2b668c7b7359b2f90973027b71b332c3.pdf
dx.doi.org/10.22075/ijnaa.2015.309
Dynamical behavior of a stage structured prey-predator model
Shashi
Kant
Department of Applied Mathematics, Delhi Technological University, Delhi 110042, India
author
Vivek
Kumar
Department of Applied Mathematics, Delhi Technological University, Delhi 110042, India
author
text
article
2016
eng
In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to obtain the conditions for which our model exhibits stability around the possible equilibrium points. Besides this a rigorous global stability analysis has been performed for our proposed model by using Li and Muldowney approach (geometric approach). Global stability conditions for the proposed model are described in the form of theorem. This is not a case study, hence the real parameters are not available for this model. However, model may be simulated by using hypothetical set of parameters. Investigation of real parameters for the proposed model is an open problem.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
231
241
https://ijnaa.semnan.ac.ir/article_311_ea84e1c2cacf1562a1872a4dda1ad2b9.pdf
dx.doi.org/10.22075/ijnaa.2015.311
An analog of Titchmarsh's theorem for the Bessel transform in the space $\mathrm{L}_{p,\alpha}(\mathbb{R}_{+})$
Mohamed
El Hamma
Department of Mathematics, Faculty of Sciences A"{i}n Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, Morocco
author
R.
Daher
Department of Mathematics, Faculty of Sciences A"{i}n Chock,
University of Hassan II, BP 5366, Maarif, Casablanca, Morocco
author
M.
Boujeddaine
Department of Mathematics and Computer Sciences, Faculty of Sciences,
Equipe d'Analyse Harmonique et Probabilit'{e}s, Universit'{e} Moulay Isma"{i}l.
BP 11201 , Zitoune, Mekn`{e}s, Morocco
author
text
article
2016
eng
Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $\mathrm{L}_{p,\alpha}(\mathbb{R}_{+})$, where $\alpha>-\frac{1}{2}$ and $1<p\leq 2$.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
243
248
https://ijnaa.semnan.ac.ir/article_312_6d7a608b8b31cc91bf4c1e508fe5d3ab.pdf
dx.doi.org/10.22075/ijnaa.2015.312
On a Hardy-Hilbert-Type Inequality with a General Homogeneous Kernel
Michael Th.
Rassias
Institute of Mathematics, University of Zurich, CH - 8057, Zurich, Switzerland & Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540, USA
author
Bicheng
Yang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P. R. China
author
text
article
2016
eng
By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
249
269
https://ijnaa.semnan.ac.ir/article_323_fdd0e926c44dc6c795dd27dfb4bef204.pdf
dx.doi.org/10.22075/ijnaa.2015.323
On the shadowing property of nonautonomous discrete systems
Hossein
Rasuoli
Young Researchers and Elite Club, Malayer Branch, Azad University, Malayer, Iran
author
text
article
2016
eng
In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of weak contractions with shadowing and h-shadowing property.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
271
277
https://ijnaa.semnan.ac.ir/article_291_3a018c19284bae1aec6ba9b21f64092c.pdf
dx.doi.org/10.22075/ijnaa.2015.291
Regularized fractional derivatives in Colombeau algebra
Mohsen
Alimohammady
Department of Mathematics, University of Mazandaran, Babolsar, Iran
author
Fariba
Fattahi Amirdehi
Department of mathematics, University of Mazandaran, babolsar, Iran
author
text
article
2016
eng
The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to a nonlinear heat equation illustrating the application of the theory.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
279
287
https://ijnaa.semnan.ac.ir/article_147_ab2bc88c6c15434692b835d36280d41a.pdf
dx.doi.org/10.22075/ijnaa.2015.147
Functionally closed sets and functionally convex sets in real Banach spaces
Madjid
Eshaghi
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
author
Hamidreza
Reisi Dezaki
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
author
Alireza
Moazzen
Kosar University of Bojnord, Bojnord, Iran
author
text
article
2016
eng
Let $X$ be a real normed space, then $C(\subseteq X)$ is functionally convex (briefly, $F$-convex), if $T(C)\subseteq \Bbb R $ is convex for all bounded linear transformations $T\in B(X,R)$; and $K(\subseteq X)$ is functionally closed (briefly, $F$-closed), if $T(K)\subseteq \Bbb R $ is closed for all bounded linear transformations $T\in B(X,R)$. We improve the Krein-Milman theorem on finite dimensional spaces. We partially prove the Chebyshev 60 years old open problem. Finally, we introduce the notion of functionally convex functions. The function $f$ on $X$ is functionally convex (briefly, $F$-convex) if epi $f$ is a $F$-convex subset of $X\times \mathbb{R}$. We show that every function $f : (a,b)\longrightarrow \mathbb{R}$ which has no vertical asymptote is $F$-convex.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
289
294
https://ijnaa.semnan.ac.ir/article_340_0cfc0fd433839779402cad7c246e5cc6.pdf
dx.doi.org/10.22075/ijnaa.2015.340
On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings
Ali
Farajzadeh
Department of Mathematics, Razi University, Kermanshah, Iran
author
text
article
2016
eng
In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [On fixed point theorems for monotone increasing vector valued mappings via scalarizing, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixed point, relaxation of the relatively compactness and the continuity on the map with replacing topological interior of the cone by the algebraic interior. Moreover, by applying Ascoli-Arzela's theorem an example in order to show that the main theorem of the paper [An intermediate value theorem for monotone operators in ordered Banach spaces, Fixed point theory and applications, 2012 (1) (2012) 1-4] may fail, is established.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
295
300
https://ijnaa.semnan.ac.ir/article_341_ffd5a9c8d2472ec439f9cf564da35d43.pdf
dx.doi.org/10.22075/ijnaa.2015.341
Completely continuous Banach algebras
Bahman
Hayati
Department of Mathematics, Malayer University, P.O. Box 16846-13114, Malayer, Iran
author
text
article
2016
eng
For a Banach algebra $\mathfrak{A}$, we introduce ~$c.c(\mathfrak{A})$, the set of all $\phi\in \mathfrak{A}^*$ such that $\theta_\phi:\mathfrak{A}\to \mathfrak{A}^*$ is a completely continuous operator, where $\theta_\phi$ is defined by $\theta_\phi(a)=a\cdot\phi$~~ for all $a\in \mathfrak{A}$. We call $\mathfrak{A}$, a completely continuous Banach algebra if $c.c(\mathfrak{A})=\mathfrak{A}^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an open problem raised for the first time by J.E Gale, T.J. Ransford and M. C. White: Is there exist an infinite dimensional amenable Banach algebra whose underlying Banach space is reflexive? We prove that a reflexive, amenable, completely continuous Banach algebra with the approximation property is trivial.
International Journal of Nonlinear Analysis and Applications
Semnan University
2008-6822
7
v.
1
no.
2016
301
308
https://ijnaa.semnan.ac.ir/article_383_3bb2ce040cb0b5b1b2133ec62d0d7465.pdf
dx.doi.org/10.22075/ijnaa.2016.383