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 , 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&#039;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