Abstract
In this paper, we study the convergence of implicit Mann iteration processes with bounded perturbations for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the △-convergence results of implicit Mann iteration schemes with bounded perturbations for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Mann iteration schemes with bounded perturbations for nonexpansive semigroups in CAT(0) spaces. The results presented in this paper extend and enrich the existing literature.MSC:47H05, 47H10, 47J25.
Highlights
Let (X, d) be a metric space and K be a subset of X
For each n ∈ N, let Tn : K → K be nonexpansive mappings and denote the common fixed points set of the family {Tn} by family of mappings is said to be uniformly asymptotically regular if, for any bounded subset B of K, lim sup d n→∞ z∈B
We extend the strong convergence result in [ ] and establish the -convergence results of implicit Mann type approximation for nonexpansive semigroups in CAT( ) spaces
Summary
Let (X, d) be a metric space and K be a subset of X. Cho et al [ ] studied the strong convergence of an explicit Mann iteration sequence {zn} for approximating a common fixed point of in a CAT( ) space, where {zn} is generated by the following iterative scheme for a nonexpansive semigroup = {T(t) : t ∈ R+}: z ∈ K , zn = αzn– ⊕ ( – α)T(tn)zn– , ∀n ≥ , where α ∈ ( , ) and {tn} ⊂ R+.
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