2015
6
2
2
0
Random differential inequalities and comparison principles for nonlinear hybrid random differential equations
2
2
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.
1

1
19


Bapurao C.
Dhage
Kasubai, Gurukul Colony, Ahmedpur413 515, Dist: Latur, Maharashtra, India
Kasubai, Gurukul Colony, Ahmedpur413 515,
Iran
bcdhage@gmail.com


Ram G.
Metkar
Kasubai, Gurukul Colony, Ahmedpur413 515, Dist: Latur, Maharashtra, India
Kasubai, Gurukul Colony, Ahmedpur413 515,
Iran
kosmalaw@bellsouth.net
Random differential inequalities
existence theorem
comparison principle
extremal solutions
Quadratic $rho$functional inequalities in $beta$homogeneous normed spaces
2
2
In cite{p}, Park introduced the quadratic $rho$functional inequalitiesbegin{eqnarray}label{E01}&& f(x+y)+f(xy)2f(x)2f(y) \ && qquad le leftrholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{xy}{2}right) f(x)  f(y)right)right, nonumberend{eqnarray}where $rho$ is a fixed complex number with $rho<1$,andbegin{eqnarray}label{E02}&& left2 fleft(frac{x+y}{2}right) + 2 fleft(frac{xy}{2}right) f(x)  f(y)right \ && qquad le rho(f(x+y)+f(xy)2f(x)2f(y)) , nonumberend{eqnarray}where $rho$ is a fixed complex number with $rho<frac{1}{2}$.In this paper, we prove the HyersUlam stability of the quadratic $rho$functional inequalities (0.1) and (0.2) in $beta$homogeneous complex Banach spaces and prove the HyersUlam stability of quadratic $rho$functional equations associated with the quadratic $rho$functional inequalities(0.1) and (0.2) in $beta$homogeneous complex Banach spaces.
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21
26


Choonkil
Park
Department of Mathematics, Research Institute for Natural Sciences,
Hanyang University, Seoul 133791, Korea
Department of Mathematics, Research Institute
Iran
baak@hanyang.ac.kr


Sang Og
Kim
Department of Mathematics,
Hallym University,
Chuncheon 2007021, Korea
Department of Mathematics,
Hallym University,
Chun
Iran
sokim@hallym.ac.kr


Jung Rye
Lee
Department of Mathematics,
Daejin University,
Kyeonggi 487711, Korea
Department of Mathematics,
Daejin University,
Kyeo
Iran
jrlee@daejin.ac.kr


Dong Yun
Shin
Department of Mathematics,
University of Seoul,
Seoul 130743, Korea.
Department of Mathematics,
University of
Iran
dyshin@uos.ac.kr
HyersUlam stability
$beta$homogeneous space
quadratic $rho$functional equation
quadratic $rho$functional inequality
An inequality related to $eta$convex functions (II)
2
2
Using the notion of etaconvex functions as generalization of convex functions, we estimate the difference between the middle and right terms in HermiteHadamardFejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.
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27
33


Madjid
Eshaghi
Department of Mathematics, Semnan University, P.O.Box. 35195363, Semnan, Iran.
Department of Mathematics, Semnan University,
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.
Mathematics, College of Engineering &
Iran
sever.dragomir@vu.edu.au


Mohsen
Rostamian Delavar
Department of Mathematics, Semnan University, P.O.Box. 35195363, Semnan, Iran.
Department of Mathematics, Semnan University,
Iran
rostamian333@gmail.com
etaconvex function
HermiteHadamardFejer inequality
Polarization constant $mathcal{K}(n,X)=1$ for entire functions of exponential type
2
2
In this paper we will prove that if $L$ is a continuous symmetric nlinear form on a Hilbert space and $widehat{L}$ is the associated continuous nhomogeneous 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 $L in {mathcal{L}}^{s}left(^{n}Xright)$, 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.
1

35
45


A.
Pappas
Civil Engineering Department, School of Technological Applications, Piraeus University of Applied Sciences (Technological Education Institute of Piraeus), GR 11244, Egaleo, Athens, Greece
Civil Engineering Department, School of Technologi
Iran
alpappas@teipir.gr


P.
Papadopoulos
adepartment of electronics engineering, school of technological applications, technological educational institution (tei)
of piraeus, gr 11244, egaleo, athens, greece.
adepartment of electronics engineering, school
Iran
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
Department of Electronics Engineering, School
Iran
athens@teipir.gr
Polarization constants
polynomials on Banach spaces
polarization formulas
An assessment of a semi analytical AG method for solving twodimension nonlinear viscous flow
2
2
In this investigation, attempts have been made to solve twodimension 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. RugeKutta 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.
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47
64


S. Tahernejad
Ledari
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
Department of Mechanical Engineering, Babol
Iran


H.
H. Mirgolbabaee
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
Department of Mechanical Engineering, Babol
Iran


Davood
Domiri Ganji
Department of Mechanical Engineering, Babol University of Technology,P.O. Box 484, Babol, Iran
Department of Mechanical Engineering, Babol
Iran
ddgdavood@yahoo.com
Adomian Decomposition Method (ADM)
AkbariGanji Method (AGM)
Homotopy Perturbation Method (HPM)
Variational Iteration Method (VIM)
New existence results for a coupled system of nonlinear differential equations of arbitrary order
2
2
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.
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65
75


M.A.
Abdellaoui
umab
umab
Iran
abdellaouiamine13@yahoo.fr


Zoubir
DAHMANI
LPAM, Faculty of SEI, UMAB, University of Mostaganem, Algeria
LPAM, Faculty of SEI, UMAB, University of
Iran
zzdahmani@yahoo.fr


N.
Bedjaoui
Laboratoire LAMFA, Universit'e de Picardie Jules Vernes, INSSET St Quentin, FRANCE
Laboratoire LAMFA, Universit'e de Picardie
Iran
nabil.bedjaoui@upicardie.fr
Caputo derivative
Coupled system
Fractional differential equation
Fixed point
Existence and uniqueness results for a nonlinear differential equations of arbitrary order
2
2
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.
1

77
92


Mohamed
Houas
Faculty of Sciences and Technology, KhemisMilian University, Ain Defla, Algeria
Faculty of Sciences and Technology, KhemisMilian
Iran
houasmed@yahoo.fr


Maamar
Benbachir
Faculty of Sciences and Technology, KhemisMilian University, Ain Defla, Algeria
Faculty of Sciences and Technology, KhemisMilian
Iran
Caputo derivative
boundary value problem
Fixed point theorem
local conditions
Simulation and perturbation analysis of escape oscillator
2
2
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 frequencyamplitude relation of escape oscillator.
1

93
101


Patanjali
Sharma
Department of Education in Science & Mathematics,
Regional Institute of Education (NCERT),
Ajmer 305 004 INDIA
Department of Education in Science &
Iran
sharma.patanjali@gmail.com
Escape oscillator
Perturbation analysis
Lindstedt's method
Continuous time portfolio optimization
2
2
This paper presents dynamic portfolio model based on the Merton's optimal investmentconsumption model, which combines dynamic synthetic put option using riskfree 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 riskfree 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).
1

103
112


Alireza
Bahiraei
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Department of Mathematics, Faculty of Mathematics,
Iran
alireza.bahiraie@yahoo.com


Behzad
Abbasi
Department of Mathematics, Faculty of Mathematics, Statistics & Computer Science, Semnan University, Semnan, Iran.
Department of Mathematics, Faculty of Mathematics,
Iran


Farahnaz
Omidi
Department of Mathematics, Faculty of Mathematics, Statistics & Computer Science, Semnan University, Semnan, Iran.
Department of Mathematics, Faculty of Mathematics,
Iran


Nor Aishah
Hamzah
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia.
Institute of Mathematical Sciences, Faculty
Iran


Abdul Hadi
Yaakub
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia.
Institute of Mathematical Sciences, Faculty
Iran
Portfolio
Investment Strategy
Dynamic Optimization
Relative orders and slowly changing functions oriented growth analysis of composite entire functions
2
2
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.
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113
126


Sanjib
Datta
Department of Mathematics,University of Kalyani, Kalyani, DistNadia, PIN 741235, West Bengal, India
Department of Mathematics,University of Kalyani,
Iran
sanjib_kr_datta@yahoo.co.in


Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar,
P.S. Kotwali, DistNadia, PIN 741101, West Bengal, India.
Rajbari, Rabindrapalli, R. N. Tagore Road,
Iran
tanmaybiswas_math@rediffmail.com


Sarmila
Bhattacharyya
Jhorehat F. C. High School for Girls, P.O. Jhorehat, P.S.
Sankrail, DistHowrah, PIN 711302, West Bengal, India.
Jhorehat F. C. High School for Girls, P.O.
Iran
bsarmila@gmail.com
Entire function
Maximum modulus
maximum term
composition
Growth
relative L*order ( relative L*lower order)
slowly changing function
Orthogonal metric space and convex contractions
2
2
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].
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127
132


Maryam
Ramezani
Faculty of Mathematics, University of Bojnord, Bojnord, Iran
Faculty of Mathematics, University of Bojnord,
Iran
mar.ram.math@gmail.com
orthogonal metric space
Fixed point
convex contaction
Modified homotopy method to solve nonlinear integral equations
2
2
In this article we decide to define a modified homotopy perturbation for solving nonlinear integral equations. Almost, all of the papers that was presented to solve nonlinear problems by the homotopy method, they used from two nonlinear and linear operators. But we convert a nonlinear problem to two suitable nonlinear 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 nonlinear integral equations. For showing ability and validity proposed method we compare our results with some works.
1

133
136


Mohsen
Rabbani
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran
Department of Mathematics, Sari Branch, Islamic
Iran
mrabbani@iust.ac.ir
Homotopy perturbation
integral equations
Nonlinear
Basis Functions
Legendre Polynomials
Subordination and Superordination Properties for Convolution Operator
2
2
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.
1

137
147


Samira
Rahrovi
Department of Mathematics, Faculty of Basic Science,
University of Bonab, Bonab, Iran.
Department of Mathematics, Faculty of Basic
Iran
sarahrovi@gmail.com
Analytic function
Convolution operator
Differential subordination
Sandwich theorem
On Hilbert GolabSchinzel type functional equation
2
2
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}bSchinzel type equation$$f(x+g(x)y)=f(x)f(y), x,yin X,$$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) 196200], Jabl o'{n}ska [Bull. Aust. Math. Soc. 87 (2013), 1017] and Rezaei [Math. Ineq. Appl., 17 (2014), 249258].
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149
159


Mohamed
Tial
Faculty of Sciences, IBN TOFAIL University , KENITRA, MOROCCO.
Faculty of Sciences, IBN TOFAIL University
Iran
tialmohamed@gmail.com


Driss
Zeglami
Moulay Ismail University, ENSAM, Meknes, MOROCCO
Moulay Ismail University, ENSAM, Meknes,
Iran
zeglamidriss@yahoo.fr


Samir
Kabbaj
Faculty of Sciences, IBN TOFAIL University , KENITRA, MOROCCO.
Faculty of Sciences, IBN TOFAIL University
Iran
samkabbaj@yahoo.fr
GolabSchinzel equation
Superstability
Hilbert valued function
Hadamard product
Probabilistic analysis of the asymmetric digital search trees
2
2
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.
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161
173


Ramin
Kazemi
Department of Statistics,
Imam Khomeini International University, Iran
Department of Statistics,
Imam Khomeini
Iran
kazemi@ikiu.ac.ir


Mohammad
Vahidiasl
Department of Statistics,
Shahid Beheshti University,
Tehran, Iran
Department of Statistics,
Shahid Beheshti
Iran
m.vahidi@sbu.ac.ir
Digital search tree
profile
functional operators
Poisson variance