ORIGINAL_ARTICLE
Random differential inequalities and comparison principles for nonlinear hybrid random differential equations
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.
https://ijnaa.semnan.ac.ir/article_228_3366bac7dc01487f906c0f41f9506933.pdf
2015-06-08
1
19
10.22075/ijnaa.2015.228
Random differential inequalities
existence theorem
comparison principle
extremal solutions
Bapurao C.
Dhage
bcdhage@gmail.com
1
Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India
LEAD_AUTHOR
Ram G.
Metkar
kosmalaw@bellsouth.net
2
Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India
AUTHOR
ORIGINAL_ARTICLE
Quadratic $\rho$-functional inequalities in $\beta$-homogeneous normed spaces
In [12], Park introduced the quadratic $\rho$-functional inequalities\begin{eqnarray}\label{E01}&& \|f(x+y)+f(x-y)-2f(x)-2f(y)\| \\ && \qquad \le \left\|\rho\left(2 f\left(\frac{x+y}{2}\right) + 2 f\left(\frac{x-y}{2}\right)- f(x) - f(y)\right)\right\|, \nonumber\end{eqnarray}where $\rho$ is a fixed complex number with $|\rho|<1$,and\begin{eqnarray}\label{E02}&& \left\|2 f\left(\frac{x+y}{2}\right) + 2 f\left(\frac{x-y}{2}\right)- f(x) - f(y)\right\| \\ && \qquad \le \|\rho(f(x+y)+f(x-y)-2f(x)-2f(y))\| , \nonumber\end{eqnarray}where $\rho$ is a fixed complex number with $|\rho|<\frac{1}{2}$.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.
https://ijnaa.semnan.ac.ir/article_229_9a2f45cf266e37c07a1530b054082e97.pdf
2015-08-05
21
26
10.22075/ijnaa.2015.229
Hyers-Ulam stability
$beta$-homogeneous space
quadratic $rho$-functional equation
quadratic $rho$-functional inequality
Choonkil
Park
baak@hanyang.ac.kr
1
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea
AUTHOR
Sang Og
Kim
sokim@hallym.ac.kr
2
Department of Mathematics, Hallym University, Chuncheon 200-7021, Korea
AUTHOR
Jung Rye
Lee
jrlee@daejin.ac.kr
3
Department of Mathematics, Daejin University, Kyeonggi 487-711, Korea
LEAD_AUTHOR
Dong Yun
Shin
dyshin@uos.ac.kr
4
Department of Mathematics, University of Seoul, Seoul 130-743, Korea
AUTHOR
ORIGINAL_ARTICLE
An inequality related to $\eta$-convex functions (II)
Using the notion of $\eta$-convex functions as a 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.
https://ijnaa.semnan.ac.ir/article_251_7e96749027a543cb76a0c8816883b38a.pdf
2015-08-26
27
33
10.22075/ijnaa.2015.251
$eta$-convex function
Hermite-Hadamard-Fejer inequality
Madjid
Eshaghi
meshaghi@semnan.ac.ir
1
Department of Mathematics, Semnan University, P.O.Box. 35195-363, Semnan, Iran.
AUTHOR
S. S.
Dragomir
sever.dragomir@vu.edu.au
2
Mathematics, College of Engineering & Science Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia
AUTHOR
Mohsen
Rostamian Delavar
rostamian333@gmail.com
3
Department of Mathematics, Semnan University, P.O.Box. 35195-363, Semnan, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Polarization constant $\mathcal{K}(n,X)=1$ for entire functions of exponential type
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$$|L|=|\widehat{L}|, \forall L \in{\mathcal{L}}^{s}(^{n}X).$$If the previous relation holds for every $L \in {\mathcal{L}}^{s}\left(^{n}X\right)$, then spaces ${\mathcal{P}}\left(^{n}X\right)$ and $L \in {\mathcal{L}}^{s}(^{n}X)$ are isometric. We can also study the same problem using Fr$\acute{e}$chet derivative.
https://ijnaa.semnan.ac.ir/article_252_67988509b46f50477e7aba6e7d056fd0.pdf
2015-08-13
35
45
10.22075/ijnaa.2015.252
Polarization constants
polynomials on Banach spaces
polarization formulas
A.
Pappas
alpappas@teipir.gr
1
Civil Engineering Department, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
LEAD_AUTHOR
P.
Papadopoulos
ppapadop@teipir.gr
2
adepartment of electronics engineering, school of technological applications, technological educational institution (tei) of piraeus, gr 11244, egaleo, athens, Greece.
AUTHOR
L.
Athanasopoulou
athens@teipir.gr
3
Department of Electronics Engineering, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
AUTHOR
ORIGINAL_ARTICLE
An assessment of a semi analytical AG method for solving two-dimension nonlinear viscous flow
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.
https://ijnaa.semnan.ac.ir/article_270_2b85ea0302d462027207cbdede350c4a.pdf
2015-09-08
47
64
10.22075/ijnaa.2015.270
Adomian Decomposition Method (ADM)
Akbari-Ganji Method (AGM)
Homotopy Perturbation Method (HPM)
Variational Iteration Method (VIM)
S. Tahernejad
Ledari
1
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
AUTHOR
H.
H. Mirgolbabaee
2
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
AUTHOR
Davood
Domiri Ganji
ddg-davood@yahoo.com
3
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
New existence results for a coupled system of nonlinear differential equations of arbitrary order
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.
https://ijnaa.semnan.ac.ir/article_255_d1b3016bdc3654dc5a27898685246ce5.pdf
2015-10-17
65
75
10.22075/ijnaa.2015.255
Caputo derivative
Coupled system
Fractional differential equation
Fixed point
M.A.
Abdellaoui
abdellaouiamine13@yahoo.fr
1
LPAM, Faculty of SEI, UMAB, University of Mostaganem, Algeria
AUTHOR
Zoubir
Dahmani
zzdahmani@yahoo.fr
2
LPAM, Faculty of SEI, UMAB, University of Mostaganem, Algeria
LEAD_AUTHOR
N.
Bedjaoui
nabil.bedjaoui@u-picardie.fr
3
Laboratoire LAMFA, Universit'e de Picardie Jules Vernes, INSSET St Quentin, France
AUTHOR
ORIGINAL_ARTICLE
Existence and uniqueness results for a nonlinear differential equations of arbitrary order
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.
https://ijnaa.semnan.ac.ir/article_256_b585261373d4776c9b9bccf99bd5c1c5.pdf
2015-11-01
77
92
10.22075/ijnaa.2015.256
Caputo derivative
boundary value problem
Fixed point theorem
local conditions
Mohamed
Houas
houasmed@yahoo.fr
1
Faculty of Sciences and Technology, Khemis-Milian University, Ain Defla, Algeria
LEAD_AUTHOR
Maamar
Benbachir
2
Faculty of Sciences and Technology, Khemis-Milian University, Ain Defla, Algeria
AUTHOR
ORIGINAL_ARTICLE
Simulation and perturbation analysis of escape oscillator
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.
https://ijnaa.semnan.ac.ir/article_257_aa4bfdc2922c3d9fa1ae4f2835dcee72.pdf
2015-09-01
93
101
10.22075/ijnaa.2015.257
Escape oscillator
Perturbation analysis
Lindstedt's method
Patanjali
Sharma
sharma.patanjali@gmail.com
1
Department of Education in Science & Mathematics, Regional Institute of Education (NCERT), Ajmer 305 004, India
AUTHOR
ORIGINAL_ARTICLE
Continuous time portfolio optimization
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).
https://ijnaa.semnan.ac.ir/article_258_df756db274fd1281ef179f49e16f96e4.pdf
2015-11-01
103
112
10.22075/ijnaa.2015.258
Portfolio
Investment Strategy
Dynamic Optimization
Alireza
Bahiraei
alireza.bahiraie@yahoo.com
1
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
LEAD_AUTHOR
Behzad
Abbasi
2
Department of Mathematics, Faculty of Mathematics, Statistics & Computer Science, Semnan University, Semnan, Iran.
AUTHOR
Farahnaz
Omidi
3
Department of Mathematics, Faculty of Mathematics, Statistics & Computer Science, Semnan University, Semnan, Iran.
AUTHOR
Nor Aishah
Hamzah
4
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia
AUTHOR
Abdul Hadi
Yaakub
5
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia
AUTHOR
ORIGINAL_ARTICLE
Relative orders and slowly changing functions oriented growth analysis of composite entire functions
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 $L\equiv L(r)$ is a slowly changing function.
https://ijnaa.semnan.ac.ir/article_259_f4c48019854386ee3f1b27569e9f1837.pdf
2015-10-14
113
126
10.22075/ijnaa.2015.259
Entire function
Maximum modulus
maximum term
composition
Growth
relative L*-order ( relative L*-lower order)
slowly changing function
Sanjib
Datta
sanjib_kr_datta@yahoo.co.in
1
Department of Mathematics,University of Kalyani, Kalyani, Dist-Nadia, PIN- 741235, West Bengal, India
LEAD_AUTHOR
Tanmay
Biswas
tanmaybiswas_math@rediffmail.com
2
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, P.S.- Kotwali, Dist-Nadia, PIN- 741101, West Bengal, India
AUTHOR
Sarmila
Bhattacharyya
bsarmila@gmail.com
3
Jhorehat F. C. High School for Girls, P.O.- Jhorehat, P.S.- Sankrail, Dist-Howrah, PIN- 711302, West Bengal, India
AUTHOR
ORIGINAL_ARTICLE
Orthogonal metric space and convex contractions
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].
https://ijnaa.semnan.ac.ir/article_261_6169f4abc6b5e917baada3b9226fcd27.pdf
2015-10-21
127
132
10.22075/ijnaa.2015.261
orthogonal metric space
Fixed point
convex contaction
Maryam
Ramezani
mar.ram.math@gmail.com
1
Faculty of Mathematics, University of Bojnord, Bojnord, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Modified homotopy method to solve non-linear integral equations
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.
https://ijnaa.semnan.ac.ir/article_262_9698eaf1127597152b3064bf956e6104.pdf
2015-11-05
133
136
10.22075/ijnaa.2015.262
Homotopy perturbation
integral equations
Non-linear
Basis Functions
Legendre Polynomials
Mohsen
Rabbani
mrabbani@iust.ac.ir
1
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
AUTHOR
ORIGINAL_ARTICLE
Subordination and Superordination Properties for Convolution Operator
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.
https://ijnaa.semnan.ac.ir/article_264_d5d42119a5eecfb10a98a6d9f2ff43c4.pdf
2015-10-29
137
147
10.22075/ijnaa.2015.264
Analytic function
Convolution operator
Differential subordination
Sandwich theorem
Samira
Rahrovi
sarahrovi@gmail.com
1
Department of Mathematics, Faculty of Basic Science,
University of Bonab, Bonab, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
On Hilbert Golab-Schinzel type functional equation
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$$f(x+g(x)y)=f(x)f(y), x,y\in X,$$where $f,g:X\rightarrow K$ 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], Jab\l o\'{n}ska [Bull. Aust. Math. Soc. 87 (2013), 10-17] and Rezaei [Math. Ineq. Appl., 17 (2014), 249-258].
https://ijnaa.semnan.ac.ir/article_265_2fbd3ede87ca876ef5fffff27f63124b.pdf
2015-11-20
149
159
10.22075/ijnaa.2015.265
Golab-Schinzel equation
Superstability
Hilbert valued function
Hadamard product
Mohamed
Tial
tialmohamed@gmail.com
1
Faculty of Sciences, IBN TOFAIL University, KENITRA, Morocco
AUTHOR
Driss
Zeglami
zeglamidriss@yahoo.fr
2
Moulay Ismail University, ENSAM, Meknes, Morocco
LEAD_AUTHOR
Samir
Kabbaj
samkabbaj@yahoo.fr
3
Faculty of Sciences, IBN TOFAIL University, KENITRA, Morocco
AUTHOR
ORIGINAL_ARTICLE
Probabilistic analysis of the asymmetric digital search trees
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.
https://ijnaa.semnan.ac.ir/article_266_11e8d7699d96813d58500f0aaf6c6fbf.pdf
2015-12-06
161
173
10.22075/ijnaa.2015.266
Digital search tree
profile
functional operators
Poisson variance
Ramin
Kazemi
kazemi@ikiu.ac.ir
1
Department of Statistics,
Imam Khomeini International University, Iran
LEAD_AUTHOR
Mohammad
Vahidi-asl
m.vahidi@sbu.ac.ir
2
Department of Statistics, Shahid Beheshti University, Tehran, Iran
AUTHOR