Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
06
08
Random differential inequalities and comparison principles for nonlinear hybrid random differential equations
1
19
EN
Bapurao C.
Dhage
Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India
bcdhage@gmail.com
Ram G.
Metkar
Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India
kosmalaw@bellsouth.net
10.22075/ijnaa.2015.228
In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities have been proved for an IVP of first order hybrid random differential equations with the linear perturbation of second type. A comparison theorem is proved and applied to prove the uniqueness of random solution for the considered perturbed random differential equation. Finally an existence of extremal random solution is obtained in between the given upper and lower random solutions.
Random differential inequalities,existence theorem,comparison principle,extremal solutions
https://ijnaa.semnan.ac.ir/article_228.html
https://ijnaa.semnan.ac.ir/article_228_3366bac7dc01487f906c0f41f9506933.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
08
05
Quadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces
21
26
EN
Choonkil
Park
Department of Mathematics, Research Institute for Natural Sciences,
Hanyang University, Seoul 133-791, Korea
baak@hanyang.ac.kr
Sang Og
Kim
Department of Mathematics,
Hallym University,
Chuncheon 200-7021, Korea
sokim@hallym.ac.kr
Jung Rye
Lee
Department of Mathematics,
Daejin University,
Kyeonggi 487-711, Korea
jrlee@daejin.ac.kr
Dong Yun
Shin
Department of Mathematics,
University of Seoul,
Seoul 130-743, Korea.
dyshin@uos.ac.kr
10.22075/ijnaa.2015.229
In cite{p}, Park introduced the quadratic $rho$-functional inequalities<br />begin{eqnarray}label{E01}<br />&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) - f(y)right)right|, nonumber<br />end{eqnarray}<br />where $rho$ is a fixed complex number with $|rho|<1$,<br />and<br />begin{eqnarray}label{E02}<br />&& left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) - f(y)right| \ && qquad le |rho(f(x+y)+f(x-y)-2f(x)-2f(y))| , nonumber<br />end{eqnarray}<br />where $rho$ is a fixed complex number with $|rho|<frac{1}{2}$.<br /><br />In this paper, we prove the Hyers-Ulam stability of the quadratic $rho$-functional inequalities (0.1) and (0.2) in $beta$-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of quadratic $rho$-functional equations associated with the quadratic $rho$-functional inequalities(0.1) and (0.2) in $beta$-homogeneous complex Banach spaces.
Hyers-Ulam stability,$beta$-homogeneous space,quadratic $rho$-functional equation,quadratic $rho$-functional inequality
https://ijnaa.semnan.ac.ir/article_229.html
https://ijnaa.semnan.ac.ir/article_229_9a2f45cf266e37c07a1530b054082e97.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
08
26
An inequality related to $eta$-convex functions (II)
27
33
EN
Madjid
Eshaghi
Department of Mathematics, Semnan University, P.O.Box. 35195-363, Semnan, Iran.
meshaghi@semnan.ac.ir
S. S.
Dragomir
Mathematics, College of Engineering & Science Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia.
Urladdr: http://rgmia.org/dragomir.
sever.dragomir@vu.edu.au
Mohsen
Rostamian Delavar
Department of Mathematics, Semnan University, P.O.Box. 35195-363, Semnan, Iran.
rostamian333@gmail.com
10.22075/ijnaa.2015.251
Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.
eta-convex function,Hermite-Hadamard-Fejer inequality
https://ijnaa.semnan.ac.ir/article_251.html
https://ijnaa.semnan.ac.ir/article_251_7e96749027a543cb76a0c8816883b38a.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
08
13
Polarization constant $mathcal{K}(n,X)=1$ for entire functions of exponential type
35
45
EN
A.
Pappas
Civil Engineering Department, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
alpappas@teipir.gr
P.
Papadopoulos
adepartment of electronics engineering, school of technological applications, technological educational institution (tei)
of piraeus, gr 11244, egaleo, athens, greece.
ppapadop@teipir.gr
L.
Athanasopoulou
Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
athens@teipir.gr
10.22075/ijnaa.2015.252
In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have that<br />$$<br />|L|=|widehat{L}|,;forall ;; L in<br />{mathcal{L}}^{s}(^{n}X);.<br />$$<br />If the previous relation holds for every $L in {mathcal{L}}^{s}left(^{n}Xright)$, then spaces ${mathcal{P}}left(^{n}Xright)$ and $L in {mathcal{L}}^{s}(^{n}X)$ are isometric. We can also study the same problem using Fr$acute{e}$chet derivative.
Polarization constants,polynomials on Banach spaces,polarization formulas
https://ijnaa.semnan.ac.ir/article_252.html
https://ijnaa.semnan.ac.ir/article_252_67988509b46f50477e7aba6e7d056fd0.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
09
08
An assessment of a semi analytical AG method for solving two-dimension nonlinear viscous flow
47
64
EN
S. Tahernejad
Ledari
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
H.
H. Mirgolbabaee
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
Davood
Domiri Ganji
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
ddg-davood@yahoo.com
10.22075/ijnaa.2015.270
In this investigation, attempts have been made to solve two-dimension nonlinear viscous flow between slowly expanding or contracting walls with weak permeability by utilizing a semi analytical Akbari Ganji's Method (AGM). As regard to previous papers, solving of nonlinear equations is difficult and the results are not accurate. This new approach is emerged after comparing the achieved solutions with numerical method and exact solution. Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. Results illustrate, this method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods. Ruge-Kutta numerical method, Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM) have been applied to make this comparison. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.
Adomian Decomposition Method (ADM),Akbari-Ganji Method (AGM),Homotopy Perturbation Method (HPM),Variational Iteration Method (VIM)
https://ijnaa.semnan.ac.ir/article_270.html
https://ijnaa.semnan.ac.ir/article_270_2b85ea0302d462027207cbdede350c4a.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
10
17
New existence results for a coupled system of nonlinear differential equations of arbitrary order
65
75
EN
M.A.
Abdellaoui
umab
abdellaouiamine13@yahoo.fr
Zoubir
DAHMANI
LPAM, Faculty of SEI, UMAB, University of Mostaganem, Algeria
zzdahmani@yahoo.fr
N.
Bedjaoui
Laboratoire LAMFA, Universit\'e de Picardie Jules Vernes, INSSET St Quentin, FRANCE
nabil.bedjaoui@u-picardie.fr
10.22075/ijnaa.2015.255
This paper studies the existence of solutions for a coupled system of nonlinear fractional differential equations. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.
Caputo derivative,Coupled system,Fractional differential equation,Fixed point
https://ijnaa.semnan.ac.ir/article_255.html
https://ijnaa.semnan.ac.ir/article_255_d1b3016bdc3654dc5a27898685246ce5.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
11
01
Existence and uniqueness results for a nonlinear differential equations of arbitrary order
77
92
EN
Mohamed
Houas
Faculty of Sciences and Technology, Khemis-Milian University, Ain Defla, Algeria
houasmed@yahoo.fr
Maamar
Benbachir
Faculty of Sciences and Technology, Khemis-Milian University, Ain Defla, Algeria
10.22075/ijnaa.2015.256
This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.
Caputo derivative,boundary value problem,Fixed point theorem,local conditions
https://ijnaa.semnan.ac.ir/article_256.html
https://ijnaa.semnan.ac.ir/article_256_b585261373d4776c9b9bccf99bd5c1c5.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
09
01
Simulation and perturbation analysis of escape oscillator
93
101
EN
Patanjali
Sharma
Department of Education in Science \& Mathematics,
Regional Institute of Education (NCERT),
Ajmer 305 004 INDIA
sharma.patanjali@gmail.com
10.22075/ijnaa.2015.257
The dynamical behaviour of the forced escape oscillator, which depends on the parameter values we considered, have been studied numerically using the techniques of phase portraits and Poincar'{e} sections. Also, we employed perturbation methods such as Lindstedt's method to obtain the frequency-amplitude relation of escape oscillator.
Escape oscillator,Perturbation analysis,Lindstedt's method
https://ijnaa.semnan.ac.ir/article_257.html
https://ijnaa.semnan.ac.ir/article_257_aa4bfdc2922c3d9fa1ae4f2835dcee72.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
11
01
Continuous time portfolio optimization
103
112
EN
Alireza
Bahiraei
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
alireza.bahiraie@yahoo.com
Behzad
Abbasi
Department of Mathematics, Faculty of Mathematics, Statistics & Computer Science, Semnan University, Semnan, Iran.
Farahnaz
Omidi
Department of Mathematics, Faculty of Mathematics, Statistics & Computer Science, Semnan University, Semnan, Iran.
Nor Aishah
Hamzah
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia.
Abdul Hadi
Yaakub
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia.
10.22075/ijnaa.2015.258
This paper presents dynamic portfolio model based on the Merton's optimal investment-consumption model, which combines dynamic synthetic put option using risk-free and risky assets. This paper is extended version of methodological paper published by Yuan Yao (2012). Because of the long history of the development of foreign financial market, with a variety of financial derivatives, the study on theory or empirical analysis of portfolio insurance focused on how best can portfolio strategies be used in minimizing risk and market volatility. In this paper, stock and risk-free assets are used to replicate options and to establish a new dynamic model to analyze the implementation of the dynamic process of investors' actions using dynamic replication strategy. Our results show that investors' optimal strategies of portfolio are not dependent on their wealth, but are dependent on market risk and this new methodology is broaden in compare to paper of Yuan Yao (2012).
Portfolio,Investment Strategy,Dynamic Optimization
https://ijnaa.semnan.ac.ir/article_258.html
https://ijnaa.semnan.ac.ir/article_258_df756db274fd1281ef179f49e16f96e4.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
10
14
Relative orders and slowly changing functions oriented growth analysis of composite entire functions
113
126
EN
Sanjib
Kumar
Datta
Department of Mathematics,University of Kalyani, Kalyani, Dist-Nadia, PIN- 741235, West Bengal, India
sanjib_kr_datta@yahoo.co.in
Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar,
P.S.- Kotwali, Dist-Nadia, PIN- 741101, West Bengal, India.
tanmaybiswas_math@rediffmail.com
Sarmila
Bhattacharyya
Jhorehat F. C. High School for Girls, P.O.- Jhorehat, P.S.-
Sankrail, Dist-Howrah, PIN- 711302, West Bengal, India.
bsarmila@gmail.com
10.22075/ijnaa.2015.259
In the paper we establish some new results depending on the comparative growth properties of composition of entire functions using relative $L^{ast }$-order (relative $L^{ast }$-lower order) as compared to their corresponding left and right factors where $Lequiv Lleft( rright) $ is a slowly changing function.
Entire function,Maximum modulus,maximum term,composition,Growth,relative L*-order ( relative L*-lower order),slowly changing function
https://ijnaa.semnan.ac.ir/article_259.html
https://ijnaa.semnan.ac.ir/article_259_f4c48019854386ee3f1b27569e9f1837.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
10
21
Orthogonal metric space and convex contractions
127
132
EN
Maryam
Ramezani
Faculty of Mathematics, University of Bojnord, Bojnord, Iran
mar.ram.math@gmail.com
10.22075/ijnaa.2015.261
In this paper, generalized convex contractions on orthogonal metric spaces are stablished in whath might be called their definitive versions. Also, we show that there are examples which show that our main theorems are genuine generalizations of Theorem 3.1 and 3.2 of [M.A. Miandaragh, M. Postolache and S. Rezapour, {it Approximate fixed points of generalized convex contractions}, Fixed Point Theory and Applications 2013, 2013:255].
orthogonal metric space,Fixed point,convex contaction
https://ijnaa.semnan.ac.ir/article_261.html
https://ijnaa.semnan.ac.ir/article_261_6169f4abc6b5e917baada3b9226fcd27.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
11
05
Modified homotopy method to solve non-linear integral equations
133
136
EN
Mohsen
Rabbani
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
mrabbani@iust.ac.ir
10.22075/ijnaa.2015.262
In this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. Almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. But we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as Legendre polynomials, expansion functions, trigonometric functions and etc. In the proposed method we obtain all of the solutions of the non-linear integral equations. For showing ability and validity proposed method we compare our results with some works.
Homotopy perturbation,integral equations,Non-linear,Basis Functions,Legendre Polynomials
https://ijnaa.semnan.ac.ir/article_262.html
https://ijnaa.semnan.ac.ir/article_262_9698eaf1127597152b3064bf956e6104.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
10
29
Subordination and Superordination Properties for Convolution Operator
137
147
EN
Samira
Rahrovi
Department of Mathematics, Faculty of Basic Science,
University of Bonab, Bonab, Iran.
sarahrovi@gmail.com
10.22075/ijnaa.2015.264
In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.
Analytic function,Convolution operator,Differential subordination,Sandwich theorem
https://ijnaa.semnan.ac.ir/article_264.html
https://ijnaa.semnan.ac.ir/article_264_d5d42119a5eecfb10a98a6d9f2ff43c4.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
11
20
On Hilbert Golab-Schinzel type functional equation
149
159
EN
Mohamed
Tial
Faculty of Sciences, IBN TOFAIL University , KENITRA, MOROCCO.
tialmohamed@gmail.com
Driss
Zeglami
Moulay Ismail University, ENSAM, Meknes, MOROCCO
zeglamidriss@yahoo.fr
Samir
Kabbaj
Faculty of Sciences, IBN TOFAIL University , KENITRA, MOROCCO.
samkabbaj@yahoo.fr
10.22075/ijnaa.2015.265
Let $X$ be a vector space over a field $K$ of real or complex numbers. We will prove the superstability of the following Go{l}c{a}b-Schinzel type equation<br />$$<br />f(x+g(x)y)=f(x)f(y), x,yin X,<br />$$<br />where $f,g:Xrightarrow K$ are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitrary Hilbert space with the Hadamard product. Our result refers to papers by Chudziak and Tabor [J. Math. Anal. Appl. 302 (2005) 196-200], Jabl o'{n}ska [Bull. Aust. Math. Soc. 87 (2013), 10-17] and Rezaei [Math. Ineq. Appl., 17 (2014), 249-258].
Golab-Schinzel equation,Superstability,Hilbert valued function,Hadamard product
https://ijnaa.semnan.ac.ir/article_265.html
https://ijnaa.semnan.ac.ir/article_265_2fbd3ede87ca876ef5fffff27f63124b.pdf
Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
6
2
2015
12
06
Probabilistic analysis of the asymmetric digital search trees
161
173
EN
Ramin
Kazemi
Department of Statistics,
Imam Khomeini International University, Iran
kazemi@ikiu.ac.ir
Mohammad
Qasem
Vahidi-asl
Department of Statistics,
Shahid Beheshti University,
Tehran, Iran
m.vahidi@sbu.ac.ir
10.22075/ijnaa.2015.266
In this paper, by applying three functional operators the previous results on the (Poisson) variance of the external profile in digital search trees will be improved. We study the profile built over $n$ binary strings generated by a memoryless source with unequal probabilities of symbols and use a combinatorial approach for studying the Poissonized variance, since the probability distribution of the profile is unknown.
Digital search tree,profile,functional operators,Poisson variance
https://ijnaa.semnan.ac.ir/article_266.html
https://ijnaa.semnan.ac.ir/article_266_11e8d7699d96813d58500f0aaf6c6fbf.pdf