فهرست مطالب
 Volume:7 Issue: 1, 2015
 تاریخ انتشار: 1394/09/30
 تعداد عناوین: 29


Pages 114In 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

Pages 1520In 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

Pages 2129A 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

Pages 3143The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular doubleband matrices uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular doubleband matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics. 234(2010) 13871394].Keywords: Spectrum of an operator, matrix mapping, sequence space

Pages 4551The 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) 330339].Keywords: Nonexpansive mapping, Common fixed point, reciprocal continuous, weak reciprocal continuous

Pages 5362In 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

Pages 6375begin{abstract} Using the fixed point method, we prove the generalized HyersUlamRassias stability of the following functional equation in multiBanach spaces: begin{equation} sum_{j = 1}^{n}fBig(2 x_{j} + sum_{i = 1, ineq j}^{n} x_{i}Big) = (n6) 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

Pages 7785In 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

Pages 8792In this paper, we are interested to study the SineGordon 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

Pages 93101Our 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 DiniLipschitz 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 DiniLipschitz condition in $L^{p}$.Keywords: Dini, Lipschitz functions, Jacobi operator, Jacobi transform

Pages 103109Fractional 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

Pages 111130The 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 wellknown 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

Pages 131140Let $lambda_1,dots,lambda_n$ 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

Pages 141145For 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 $(ns)$. 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 wellknown results.Keywords: Polynomial, Zeros, $s^{th}$ derivative

Pages 147153In 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

Pages 155165We 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

Pages 167181In this paper, we obtain the general solution and the generalized HyersUlamRassias stability in random normed spaces, in nonArchimedean 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_{mk+1}=i_{mk}+1}) f(\sum^{m}_{i=1, i\neq i_{1},...,i_{mk+1}} x_{i}\sum^{mk+1}_{r=1} x_{i_{r}})\\& \hspace {2.8cm}+f(\sum^{m}_{i=1} x_{i})2^{m1} f(x_{1})=0\end{align*}where $m \geq 2$ is an integer number.Keywords: Additive function, $p$, Banach spaces, Random normed spaces, Non, Archimedean spaces, Fixed point method, Generalized Hyers, Ulam stability

Pages 183194In 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

Pages 195205We 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 semisymmetric 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

Pages 207218In this paper, we discuss about existence of solution for integrodifferential system and then we solve it by using the PetrovGalerkin method. In the PetrovGalerkin method choosing the trial and test space is important, so we use Alpert multiwavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multiwavelet 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

Pages 219224We first obtain some properties of a fundamentally nonexpansive selfmapping 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

Pages 225230In 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

Pages 231241In this paper, a new stage structured preypredator 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

Pages 243248Using 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
Pages 249269
By the method of weight coefficients and techniques of real analysis, aHardyHilberttype 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
Pages 271277
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 hshadowing property.
Keywords:
Nonautonomous discrete system, nonautonomos difference equation, shadowing property
Pages 279287
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
Pages 289294
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 KreinMilman 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
Pages 295300
In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [\textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333340] with containing the uniqueness, convergent of each iteration to the fixed point, relaxation of the relatively compactness and the continuity on the map with replacing topological interior of the cone by the algebraic interior. Moreover, by applying AscoliArzela's theorem an example in order to show that the main theorem of the paper [\textit{An intermediate value theorem for monotone operators in ordered Banach spaces}, Fixed point theory and applications, 2012 (1) (2012) 14] may fail, is established.
Keywords:
intermediate value theorem, fixed point, increasing mapping, algebraic interior, normal cone