Total quasi-ϕ-asymptotically nonexpansive semigroups and strong convergence theorems in Banach spaces

Total quasi-φ-asymptotically nonexpansive semigroups and strong convergence theorems in Banach spaces

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 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 theorems of total quasi-ϕ-asymptotically nonexpansive semi-groups in Banach spaces

The purpose of this paper is to introduce and study total quasiφ -asymptotically nonexpansive semi-groups and to modify the Halpern-Mann-type iteration algorithm for the new semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results announced by many authors [1,...

Convergence 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.