Strong convergence theorem for total quasi-ϕ-asymptotically nonexpansive mappings in a Banach space

Strong Convergence Theorem for Infinite Family of Total Quasi-φ-asymptotically Nonexpansive Multi-valued Mappings

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

Strong 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...

Strong convergence for total quasi-φ-asymptotically nonexpansive semigroups in Banach spaces

Definition . Let T : C → C be a mapping. T is said to be total asymptotically nonexpansive if there exist sequences {μn}, {νn} with μn,νn →  as n → ∞ and a strictly increasing continuous function ψ : R → R with ψ() =  such that ‖Tnx – Tny‖ ≤ ‖x – y‖ +μnψ(‖x – y‖) + νn holds for all x, y ∈ C and all n ∈N. T is said to be total asymptotically quasi-nonexpansive if F(T) = ∅, there exist seque...

Strong Convergence Theorems for a Countable Family of Total Quasi-φ-Asymptotically Nonexpansive Nonself Mappings

The purpose of this paper is to introduce a class of total quasi-φ-asymptotically nonexpansivenonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the co...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition