INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS
Year:2016 | Volume:7 | Issue:2|Papers Count:30

By the method of weight coe cients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the reverses and some particular cases are also considered.

Some functional inequalities in variable exponent Lebesgue spaces are presented. The bi-weighted modular inequality with variable exponent p(: ) for the Hardy operator restricted to non-increasing function which is....

For a Banach algebra A, A00 is (􀀀 1)-weakly amenable if A0 is a Banach A00-bimodule and H1(A00; A0) = f0g. In this paper we prove some important properties of this notion, for instance if A00 is (􀀀 1)-weakly amenable then A is essential and there is no non-zero point derivation on A. We also give some examples, namely, the second dual of every C-algebras is (􀀀 1)-weakly amenable. Finally, we study the relationships between the (􀀀 1)-weakly amenability of A00 and the weak amenability of A00 or A.

In this work, we formulate Chatterjea contractions using graphs in metric spaces endowed with a graph and investigate the existence of  xed points for such mappings under two di erent hypotheses. We also discuss the uniqueness of the  xed point. The given result here is a generalization of Chatterjea's  xed point theorem from metric spaces to metric spaces endowed with a graph.

This paper presents an approach for solving nonlinear stochastic di erential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of 2m + 2 equations and 2m + 2 unknowns. Then, the error analysis is proved. Finally, numerical examples illustrate applicability and accuracy of the presented method.

In the present article, we propose the (p; q) variant of genuine Baskakov Durrmeyer operators. We obtain moments and establish some direct results, which include weighted approximation and results in terms of modulus of continuity of second order.

The main purpose of this paper is to obtain su cient conditions for existence of points of coincidence and common  xed points for three self mappings in b-metric spaces. Next, we obtain cone b-metric version of these results by using a scalarization function. Our results extend and generalize several well known comparable results in the existing literature.

In this paper we introduce new modi ed implicit and explicit algorithms and prove strong convergence of the two algorithms to a common  xed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real re exive Banach space with a uniformly G^ateaux di erentiable norm. Our result is applicable in Lp(`p) spaces, 1 < p < 1 and consequently in sobolev spaces.

Let A be an algebra. A linear mapping  : A! A is called a derivation if  (ab) =  (a)b + a (b) for each a; b 2 A. Given two derivations  and  0 on a C-algebra A, we prove that there exists a derivation
on A such that   0 =
2 if and only if either  0 = 0 or  = s 0 for some s 2 C.

In this paper, given a poset (X;  ), we introduce some drifts on a groupoid (X;  ) with respect to (X;  ), and we obtain several properties of these drifts related to the notion of Bin(X). We discuss some connections between fuzzy subalgebras and upward drifts.

In this paper, we  nd explicit solution to the operator equation TXS 􀀀 SX T = A in the general setting of the adjointable operators between Hilbert C-modules, when T; S have closed ranges and S is a self adjoint operator.

Let f; g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative ( ;  )􀀀 derivation is additive.

Let RR be a commutative ring with identity, let AA and BB be two RR-algebras and φ : B⟶ Aφ : B⟶ A be an RR-additive algebra homomorphism. We introduce a new algebra A×φ BA×φ B, and give some basic properties of this algebra. Generalized 22-cocycle derivations on A×φ BA×φ B are studied. Accordingly, A×φ BA×φ B is considered from the perspective of Banach algebras.

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H\"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main results.

In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.

Using  xed point method, we prove some new stability results for Lie ( ;  ; )-derivations and Lie C-algebra homomorphisms on Lie C-algebras associated with the Euler-Lagrange type additive functional equation....

In this paper we apply the technique of measures of noncompactness to the theory of in nite system of integral equations in the Fr echet spaces. Our aim is to provide a few generalization of Tychono  xed point theorem and prove the existence of solutions for in nite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tychono  xed point theorem. Also, we present an example of nonlinear integral equations to show the e ciency of our results. Our results extend several comparable results obtained in the previous literature.

In this paper, sufficient conditions for the existence of common fixed points for a compatible pair of self maps of Gregus type in the framework of convex metric spaces have been obtained. Also, established the existence of common fixed points for a pair of compatible mappings of type (B) and consequently for compatible mappings of type (A). The proved results generalize and extend some of the well known results of the literature.

In the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. The basic assumption is that the class of functions that we investigate here, except the verification of Dirichlet's principles, is concurrently able to be expanded in Taylor's representation, over a particular interval of their domain of definition. Thus, we shall take into account the simultaneous validity of these two properties over this interval, in order to obtain an alternative equivalent representation of the corresponding harmonic decomposition for this category of functions. In the sequel, we shall also implement this resultant formula in the investigation of turbulence spectrum of eddies according to known from literature Von Karman's formulation, making the additional assumption that during the evolution of such stochastic dynamic effects with respect to time, the occasional time-returning period can be actually supposed to tend to infinity.

In this paper, we study Projected non-stationary Simultaneous It-erative Reconstruction Techniques (P-SIRT). Based on algorithmic op-erators, convergence result are adjusted with Opial’ s Theorem. The advantages of P-SIRT are demonstrated on examples taken from to-mographic imaging.

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

In this paper, differential transform method (DTM) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in HIV infections of cell. Intervals of validity of the solution will be extended by using Pade approximation. The results also will be compared with those results obtained by Runge-Kutta method. The technique is described and is illustrated with one numerical example. The numerical results shown that the reliability and efficiency of the method.

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation ∫ Sf(σ (y)xt)dμ (t)− ∫ Sf(xyt)dμ (t)=2f(x)f(y), x, y∈ S, ∫ Sf(σ (y)xt)dμ (t)− ∫ Sf(xyt)dμ (t)=2f(x)f(y), x, y∈ S, where SS is a semigroup, σ σ is an involutive morphism of SS, and μ μ is a complex measure that is linear combinations of Dirac measures (δ zi)i∈ I(δ zi)i∈ I, such that for all i∈ Ii∈ I, zizi is contained in the center of SS. (2) We determine the complex-valued continuous solutions of the following variant of d'Alembert's functional equation ∫ Sf(xty)dυ (t)+∫ Sf(σ (y)tx)dυ (t)=2f(x)f(y), x, y∈ S, ∫ Sf(xty)dυ (t)+∫ Sf(σ (y)tx)dυ (t)=2f(x)f(y), x, y∈ S, where SS is a topological semigroup, σ σ is a continuous involutive automorphism of SS, and υ υ is a complex measure with compact support and which is σ σ-invariant. (3) We prove the superstability theorems of the first functional equation.

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of the local center manifold theorem, the stable manifold theorem and the Hartman-Grobman theorem to the scope of fractional differential systems. These latter two theorems establish that the qualitative behavior of the solution set of a nonlinear system of fractional differential equations near an equilibrium point is typically the same as the qualitative behavior of the solution set of the corresponding linearized system near the equilibrium point. Furthermore, we discuss the stability conditions for the equilibrium points of these systems. We point out that, the fractional derivative in these systems is in the Caputo sense.

In this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium E=(x¯ , y¯ )E=(x¯ , y¯ ) of the system of two difference equations of exponential form: xn+1=a+e− (bxn+cyn)d+bxn+cyn, yn+1=a+e− (byn+cxn)d+byn+cxnxn+1=a+e− (bxn+cyn)d+bxn+cyn, yn+1=a+e− (byn+cxn)d+byn+cxn where a, b, c, da, b, c, d are positive constants and the initial values x0, y0x0, y0 are positive real values.

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed into a linear system of algebraic equations. Matrix formulation, error analysis and order of convergence of the proposed method are also discussed. Some numerical experiments are presented to demonstrate the effectiveness of the proposed method and to confirm the analytic results.

Let PP be a complex polynomial of the form P(z)=z∏ k=1n− 1(z− zk)P(z)=z∏ k=1n− 1(z− zk), where |zk|≥ 1, 1≤ k≤ n− 1|zk|≥ 1, 1≤ k≤ n− 1 then P′ (z)≠ 0P′ (z)≠ 0. If |z|<1n|z|<1n. In this paper, we present some interesting generalisations of this result.

In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. We also give an example to illustrate the obtained result.

In this paper, we establish and prove the existence of best proximity points for multivalued cyclic FF-contraction mappings in complete metric spaces. Our results improve and extend various results in literature.