Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi--Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces
نویسندگان
چکیده
منابع مشابه
Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi-φ-Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces
and Applied Analysis 3 Let X be a smooth Banach space. We always use φ : X × X → R to denote the Lyapunov functional defined by φ ( x, y ) ‖x‖ − 2〈x, Jy〉 ∥∥y∥∥2, ∀x, y ∈ X. 1.7 It is obvious from the definition of the function φ that (‖x‖ − ∥∥y∥∥)2 ≤ φ(x, y) ≤ (‖x‖ ∥∥y∥∥)2, ∀x, y ∈ X. 1.8 Following Alber 4 , the generalized projection ΠC : X → C is defined by ΠC x arg inf y∈C φ ( y, x ) , ∀x ∈ ...
متن کاملConvergence theorems of implicit iterates with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces
In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.
متن کاملStrong Convergence Theorems for Bregman Quasi–asymptotically Nonexpansive Mappings and Equilibrium Problem in Reflexive Banach Spaces
The purpose of this article is to propose an iteration algorithm for Bergman quasiasymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of reflexive Banach spaces. As applications, we apply our results to a system of equilibrium problems. The results presented in the paper improve and extend the corresponding results of Reich and Sabach...
متن کاملStrong convergence theorems for equilibrium problems and quasi-φ-asymptotically nonexpansive mappings in Banach spaces
In this paper, we introduce two modified Mann-type iterative algorithms for finding a common element of the set of common fixed points of a family of quasi-φ-asymptotically nonexpansive mappings and the set of solutions of an equilibrium problem in Banach spaces. Then we study the strong convergence of the algorithms. Our results improve and extend the corresponding results announced by many ot...
متن کاملConvergence theorems of multi-step iterative algorithm with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces
The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2012
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2012/147915