2022-05-28T08:11:58Z
https://ijnaa.semnan.ac.ir/?_action=export&rf=summon&issue=38
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Random differential inequalities and comparison principles for nonlinear hybrid random differential equations
Bapurao C.
Dhage
Ram G.
Metkar
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
2015
06
08
1
19
https://ijnaa.semnan.ac.ir/article_228_3366bac7dc01487f906c0f41f9506933.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Quadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces
Choonkil
Park
Sang Og
Kim
Jung Rye
Lee
Dong Yun
Shin
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.
Hyers-Ulam stability
$beta$-homogeneous space
quadratic $rho$-functional equation
quadratic $rho$-functional inequality
2015
08
05
21
26
https://ijnaa.semnan.ac.ir/article_229_9a2f45cf266e37c07a1530b054082e97.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
An inequality related to $eta$-convex functions (II)
Madjid
Eshaghi
S. S.
Dragomir
Mohsen
Rostamian Delavar
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.
$eta$-convex function
Hermite-Hadamard-Fejer inequality
2015
08
26
27
33
https://ijnaa.semnan.ac.ir/article_251_7e96749027a543cb76a0c8816883b38a.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Polarization constant $mathcal{K}(n,X)=1$ for entire functions of exponential type
A.
Pappas
P.
Papadopoulos
L.
Athanasopoulou
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.
Polarization constants
polynomials on Banach spaces
polarization formulas
2015
08
13
35
45
https://ijnaa.semnan.ac.ir/article_252_67988509b46f50477e7aba6e7d056fd0.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
An assessment of a semi analytical AG method for solving two-dimension nonlinear viscous flow
S. Tahernejad
Ledari
H.
H. Mirgolbabaee
Davood
Domiri Ganji
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)
2015
09
08
47
64
https://ijnaa.semnan.ac.ir/article_270_2b85ea0302d462027207cbdede350c4a.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
New existence results for a coupled system of nonlinear differential equations of arbitrary order
M.A.
Abdellaoui
Zoubir
Dahmani
N.
Bedjaoui
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
2015
10
17
65
75
https://ijnaa.semnan.ac.ir/article_255_d1b3016bdc3654dc5a27898685246ce5.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Existence and uniqueness results for a nonlinear differential equations of arbitrary order
Mohamed
Houas
Maamar
Benbachir
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
2015
11
01
77
92
https://ijnaa.semnan.ac.ir/article_256_b585261373d4776c9b9bccf99bd5c1c5.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Simulation and perturbation analysis of escape oscillator
Patanjali
Sharma
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
2015
09
01
93
101
https://ijnaa.semnan.ac.ir/article_257_aa4bfdc2922c3d9fa1ae4f2835dcee72.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Continuous time portfolio optimization
Alireza
Bahiraei
Behzad
Abbasi
Farahnaz
Omidi
Nor Aishah
Hamzah
Abdul Hadi
Yaakub
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
2015
11
01
103
112
https://ijnaa.semnan.ac.ir/article_258_df756db274fd1281ef179f49e16f96e4.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Relative orders and slowly changing functions oriented growth analysis of composite entire functions
Sanjib
Datta
Tanmay
Biswas
Sarmila
Bhattacharyya
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.
Entire function
Maximum modulus
maximum term
composition
Growth
relative L*-order ( relative L*-lower order)
slowly changing function
2015
10
14
113
126
https://ijnaa.semnan.ac.ir/article_259_f4c48019854386ee3f1b27569e9f1837.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Orthogonal metric space and convex contractions
Maryam
Ramezani
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
2015
10
21
127
132
https://ijnaa.semnan.ac.ir/article_261_6169f4abc6b5e917baada3b9226fcd27.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Modified homotopy method to solve non-linear integral equations
Mohsen
Rabbani
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
2015
11
05
133
136
https://ijnaa.semnan.ac.ir/article_262_9698eaf1127597152b3064bf956e6104.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Subordination and Superordination Properties for Convolution Operator
Samira
Rahrovi
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
2015
10
29
137
147
https://ijnaa.semnan.ac.ir/article_264_d5d42119a5eecfb10a98a6d9f2ff43c4.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
On Hilbert Golab-Schinzel type functional equation
Mohamed
Tial
Driss
Zeglami
Samir
Kabbaj
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].
Golab-Schinzel equation
Superstability
Hilbert valued function
Hadamard product
2015
11
20
149
159
https://ijnaa.semnan.ac.ir/article_265_2fbd3ede87ca876ef5fffff27f63124b.pdf
International Journal of Nonlinear Analysis and Applications
IJNAA
2015
6
2
Probabilistic analysis of the asymmetric digital search trees
Ramin
Kazemi
Mohammad
Vahidi-asl
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
2015
12
06
161
173
https://ijnaa.semnan.ac.ir/article_266_11e8d7699d96813d58500f0aaf6c6fbf.pdf