### فهرست مطالب

• Volume:7 Issue: 1, 2015
• تاریخ انتشار: 1394/09/30
• تعداد عناوین: 29
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• Dibyendu Banerjee *, Nilkanta Mondal Pages 1-14
In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results.Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of its partial derivative.
Keywords: Banach valued Dirichlet series, relative order, relative type, entire function
• S. Abbaszadeh*, M. Eshaghi Gordji Pages 15-20
In this paper, we first introduce the notion of $c$-affine functions for $c> 0$.Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.
Keywords: strongly convex function, Hahn, Banach theorem, $c$, affine functions, quadratic support
A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T: E longrightarrow E$ on a nonempty bounded closed convex subset $E$ of $mathfrak{X}$ has a fixed point. In this paper, we first show that if $X$ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (iii) $C_0 (X)$ does not have the fixed point property. We also show that if $A$ is a commutative complex $mathsf{C}^star$--algebra with nonempty carrier space, then the following statements are equivalent: (i) Carrier space of $A$ is infinite, (ii) $A$ is infinite dimensional, (iii) $A$ does not have the fixed point property. Moreover, we show that if $A$ is an infinite complex $mathsf{C}^star$--algebra (not necessarily commutative), then $A$ does not have the fixed point property.
Keywords: Banach space, $mathsf{C}^star$, algebra, fixed point property, Nonexpansive mapping, normed linear space
The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics. 234(2010) 1387-1394].
Keywords: Spectrum of an operator, matrix mapping, sequence space
• Pankaj Kumar Jhade*, A. S Saluja Pages 45-51
The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of nonexpansive type multivalued and single valued maps, European J. Pure Appl. Math., 4 (2011) 330-339].
Keywords: Nonexpansive mapping, Common fixed point, reciprocal continuous, weak reciprocal continuous
• Said Beloul Pages 53-62
In this paper, we will establish some xed point results for two pairs of self mappings satisfying generalized contractive condition by using a new concept as weak subsequential continuity with compatibility of type (E) in metric spaces, as an application the existence of unique common solution for a system of functional equations arising in system programming is proved.
Keywords: generalized contractive condition, weakly subsequentially continuous, compatible of type (E), functional equation
begin{abstract} Using the fixed point method, we prove the generalized Hyers--Ulam--Rassias stability of the following functional equation in multi-Banach spaces: begin{equation} sum_{j = 1}^{n}fBig(-2 x_{j} + sum_{i = 1, ineq j}^{n} x_{i}Big) = (n-6) fBig(sum_{i = 1}^{n} x_{i}Big) + 9 sum_{i = 1}^{n} f(x_{i}).end{equation}end{abstract}
Keywords: Fixed point method, Hyers, Ulam, Rassias stability, Multi, Banach spaces, Quadratic mapping
• Huseyin Budak*, Mehmet Sarikaya Pages 77-85
In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.
Keywords: Bounded Variation, Ostrowski type inequalities, Riemann, Stieltjes, Trapezoid Inequality
• Lalla Saadia Chadli*, Said Melliani, Abdelaziz Moujahid, Mhamed Elomari Pages 87-92
In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.
Keywords: Algebra Colombeau, Generalized functions theory, Sine, Gordon equation
• Mustapha Boujeddaine*, Said Fahlaoui, Radouan Daher Pages 93-101
Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lipschitz condition in $L^{p}$.
Keywords: Dini, Lipschitz functions, Jacobi operator, Jacobi transform
• Sabrina Taf*, Kamel Brahim Pages 103-109
Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order.The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results. Furthermore, other integral inequalities of reverse Minkowski's type are obtained for positive functions resulting in two theorems.
Keywords: Hadamard fractional integral, Fractional integral inequalities, Minkowski's inequality
• R.A. Rashwan*, S.M. Saleh Pages 111-130
The aim of this paper is to prove some common fixed point theorems for four mappings satisfying $(\psi,\varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.
Keywords: Common fixed point, rational contractions, ordered partial metric spaces, dominating, dominated mappings
• Seyed Mahmoud Manjegani Pages 131-140
‎Let $lambda_1,dots,lambda_n$ be positive real numbers such that‎ ‎$sum_{k=1}^n lambda_k=1$‎. ‎We prove that for‎ ‎any positive operators $a_1,a_2,cdots‎, ‎a_n$ in semifinite von‎ ‎Neumann algebra $M$ with faithful normal trace that $t(1) Keywords: ýSingular valuesý, ýSemifinite traceý, ýMajorisationý, ýlog, majorisation • Abdullah Mir Pages 141-145 For every$1\leq s< n$, the$s^{th}$derivative of a polynomial$P(z)$of degree$n$is a polynomial$P^{(s)}(z)$whose degree is$(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the$s^{th}$derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results. Keywords: Polynomial, Zeros,$s^{th}$derivative • Kourosh Nourouzi Pages 147-153 In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces. Keywords: Vector ultra metric space, Correspondence, fixed point • Hedayat Fathi*, S.A.R. Hosseinioun Pages 155-165 We introduce variational inequality problems on Hilbert$C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities,$C^*$-valued metric projection and fixed point theory on Hilbert$C^*$-modules is studied. Keywords: variational inequality, Hilbert$C^*$, module, metric projection, fixed point • R. Farokhzad Rostami*, S.A.R. Hoseinioun Pages 167-181 In this paper, we obtain the general solution and the generalized Hyers--Ulam--Rassias stability in random normed spaces, in non-Archimedean spacesand also in$p-Banach spaces and finally the stability via fixed point method for a functional equation\begin{align*}&D_f(x_{1},.., x_{m}):= \sum^{m}_{k=2}(\sum^{k}_{i_{1}=2}\sum^{k+1}_{i_{2}=i_{1}+1}... \sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(\sum^{m}_{i=1, i\neq i_{1},...,i_{m-k+1}} x_{i}-\sum^{m-k+1}_{r=1} x_{i_{r}})\\& \hspace {2.8cm}+f(\sum^{m}_{i=1} x_{i})-2^{m-1} f(x_{1})=0\end{align*}wherem \geq 2$is an integer number. Keywords: Additive function,$p$, Banach spaces, Random normed spaces, Non, Archimedean spaces, Fixed point method, Generalized Hyers, Ulam stability • Alireza Naeimi Sadigh*, Samaneh Ghods Pages 183-194 In this paper, we prove some coupled coincidence point theorems for mappings with the mixed monotone property and obtain the uniqueness of this coincidence point. Then we providing useful examples in Nash equilibrium. Keywords: Coupled Fixed point, Coupled coincidence Fixed point, Partially ordered sets, Cone metric space, Game theory, Nash equilibrium • Mahmood Parchetalab Pages 195-205 We classify the paracontact Riemannian manifolds that their Rieman- nian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally sym- metric spaces. Finally we study paracontact Riemannian manifolds satis- fying R(X, ξ).S = 0, where S is the Ricci tensor. Keywords: paracontact structure, Einstein structure, parasasakian • Mohsen Rabbani Pages 207-218 ‎In this paper, we discuss about existence of solution for integro-differential system and then we solve it by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in the process of discretizing and we drive a system of algebraic equations with small dimension which it leads to approximate solution with high accuracy. We compare the results with similar works and it guarantees the validity and applicability of this method. Keywords: System of Integro, differential equations, Multi, wavelet, Petrov, Galerkin, Regular pairs, Trial space, Test space • Mohammad Moosaei Pages 219-224 We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex. Keywords: fixed point, fundamentally nonexpansive mappings, nonexpansive mappings, Opial's condition, uniformly convex Banach spaces • Masoud Hadian Dehkordi, Masoud Ghods * Pages 225-230 In this paper, we introduce the (G-$\psi$) contraction in a metric space by using a graph. Let$F,T$be two multivalued mappings on$X.$Among other things, we obtain a common fixed point of the mappings$F,T$in the metric space$X$endowed with a graph$G.$Keywords: fixed point, multivalued, common(G,$psi$) contraction, directed graph • Shashi Kant*, Vivek Kumar Pages 231-241 In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to obtain the conditions for which our model exhibits stability around the possible equilibrium points. Besides this a rigorous global stability analysis has been performed for our proposed model by using Li and Muldowney approach (geometric approach). Global stability conditions for the proposed model are described in the form of theorem. This is not a case study, hence the real parameters are not available for this model. However, model may be simulated by using hypothetical set of parameters. Investigation of real parameters for the proposed model is an open problem. Keywords: Stage Structured Population, Global Stability, Local Stability • Mohamed El Hamma*, R. Daher, M. Boujeddaine Pages 243-248 Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space$\mathrm{L}_{p,\alpha}(\mathbb{R}_{+})$, where$\alpha>-\frac{1}{2}$and$1 Keywords: Bessel operator, Bessel transform, Bessel generalized translation
• Michael Th. Rassias*, Bicheng Yang Pages 249-269
By the method of weight coefficients and techniques of real analysis, aHardy-Hilbert-type inequality with a general homogeneous kernel and a bestpossible constant factor is given. The equivalent forms, the operatorexpressions with the norm, the reverses and some particular examples are alsoconsidered.
Keywords: Hardy, Hilbert, type inequality, weight coefficient, equivalent form, reverse, operator
• Hossein Rasuoli Pages 271-277
In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of weak contractions with shadowing and h-shadowing property.
Keywords: Nonautonomous discrete system, nonautonomos difference equation, shadowing property
• Mohsen Alimohammady*, Fariba Fattahi Amirdehi Pages 279-287
The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to a nonlinear heat equation illustrating the application of the theory.
Keywords: Colombeau algebra, Caputo fractional derivative, Riesz fractional derivative
• Madjid Eshaghi, Hamidreza Reisi Dezaki*, Alireza Moazzen Pages 289-294
‎Let $X$ be a real normed space, then $C(\subseteq X)$ is functionally convex (briefly, $F$-convex), if $T(C)\subseteq \Bbb R$ is convex for all bounded linear transformations $T\in B(X,R)$; and $K(\subseteq X)$ is functionally closed (briefly, $F$-closed), if $T(K)\subseteq \Bbb R$ is closed for all bounded linear transformations $T\in B(X,R)$. We improve the Krein-Milman theorem on finite dimensional spaces. We partially prove the Chebyshev 60 years old open problem. Finally, we introduce the notion of functionally convex functions. The function $f$ on $X$ is functionally convex (briefly, $F$-convex) if epi $f$ is a $F$-convex subset of $X\times \mathbb{R}$. We show that every function $f: (a,b)\longrightarrow \mathbb{R}$ which has no vertical asymptote is $F$-convex.
Keywords: ýConvex set, Chebyshev set, Krein, Milman theorem