and Applied Analysis 3 In this paper, we firstly present the definition of duality fixed point for a mapping T from E into its dual E∗ as follows. Let E be a Banach space with a single-valued generalized duality mapping Jp : E → E∗. Let T : E → E∗. An element x∗ ∈ E is said to be a generalized duality fixed point of T if Tx∗ Jpx∗. An element x∗ ∈ E is said to be a duality fixed point of T if Tx...

We establish exponential decay in Hölder norm of transfer operators applied to smooth observables uniformly and nonuniformly expanding semiflows with correlations.

We introduce composite implicit and explicit iterative algorithms for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a real smooth and uniformly convex Banach space.These composite iterative algorithms are based on Korpelevich’s extragradient method and viscosity approximation method. We first consider and ...

Abstract In this work, we prove the weak convergence of a one-step self-adaptive algorithm to solution sum two monotone operators in 2-uniformly convex and uniformly smooth real Banach spaces. We give numerical examples infinite-dimensional spaces compare our result with some existing algorithms. Finally, results extend complement several literature.

In this paper we establish the strong convergence and almost stability of the Ishikawa iteration methods with errors for the iterative approximations of either fixed points of local strongly pseudocontractive operators or solutions of nonlinear operator equations with local strongly accretive type in real uniformly smooth Banach spaces. Our convergence results extend some known results in the l...

In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-φ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Strong convergence of the sequences generated by these algorithms is proved in uniformly smooth and strictly co...

In this paper we study the hybrid iterative scheme to find a common element of a set of solutions of generalized mixed equilibrium problem, a set of common fixed points of finite family of weak relatively nonexpansive mapping, and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and g...

An upper bound q(c) for the best, under equivalent renorming, possible power type of the modulus of smoothness of a Banach space with modulus of convexity satisfying δX(ε) cε2, is found. The estimate is asymptotically sharp and is expressed in terms of linear fractional function q(c). © 2006 Elsevier Inc. All rights reserved.

The objective of this paper is to study the iterative solutions of a class of generalized co-complementarity problems in p-uniformly smooth Banach spaces, with the devotion of sunny retraction mapping, p-strongly accretive, p-relaxed accretive and Lipschitzian (or more generally uniformly continuous) mappings. Our results are new and represents a significant improvement of previously known resu...

It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure. A Banach space is said to have the fixed point property (FPP) if for every nonempty bounded closed convex C ⊂ X and every nonexpansive self-mapping T : C → C there is a fixed point of T in C. A Banach space is said to have the weak fixed point prope...