Abstract

We introduce an implicit and explicit iterative schemes for a finite family of nonexpansive semigroups with the Meir‐Keeler‐type contraction in a Banach space. Then we prove the strong convergence for the implicit and explicit iterative schemes. Our results extend and improve some recent ones in literatures.

Highlights

  • We introduce an implicit and explicit iterative schemes for a finite family of nonexpansive semigroups with the Meir-Keeler-type contraction in a Banach space

  • Let C be a nonempty subset of a Banach space E and T : C → C be a mapping

  • We denote by Fix T the set of all common fixed points of semigroup T, that is, Fix T {x ∈ C : T t x x, 0 ≤ t < ∞} and N by the set of natural numbers

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Summary

Introduction

Let C be a nonempty subset of a Banach space E and T : C → C be a mapping. We call T nonexpansive if T x − T y ≤ x − y for all x, y ∈ E.

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