Comment on “A Strong Convergence of a Generalized Iterative Method for Semigroups of Nonexpansive Mappings in Hilbert Spaces”

Saber Naseri,Farman Golkarmanesh

doi:10.1155/2011/257034

Abstract

Piri and Vaezi (2010) introduced an iterative scheme for finding a common fixed point of a semigroup of nonexpansive mappings in a Hilbert space. Here, we present that their conclusions are not original and most parts of their paper are picked up from Saeidi and Naseri (2010), though it has not been cited.

Highlights

Let S be a semigroup and B S the Banach space of all bounded real-valued functions on S with supremum norm
For each s ∈ S, the left translation operator l s on B S is defined by lsftf st for each t ∈ S and f ∈ B S
A mean μ on X is said to be left invariant if μ lsf μ f for each s ∈ S and f ∈ X

Summary

Introduction

Let S be a semigroup and B S the Banach space of all bounded real-valued functions on S with supremum norm. Piri and Vaezi 2010 introduced an iterative scheme for finding a common fixed point of a semigroup of nonexpansive mappings in a Hilbert space. A mean μ on X is said to be left invariant if μ lsf μ f for each s ∈ S and f ∈ X.

Results

Conclusion