A note on the paper: On iterations for families of asymptotically pseudocontractive mappings, Applied Mathematics Letters, 24 (2011), 33-38

TL;DR

This paper identifies a flaw in a previous proof regarding iterations of asymptotically pseudocontractive mappings and proposes a corrected condition to address the issue.

Contribution

It provides a counterexample to a proof in earlier work and introduces an alternative condition to fix the identified flaw.

Findings

Counterexample invalidates the original proof

Proposes a corrected condition for the theorem

Clarifies the theoretical understanding of asymptotically pseudocontractive mappings

Abstract

It is our aim in this note to give a counter example to an argument used in the proof of the main theorem of the paper: On iterations for families of asymptotically pseudocontractive mappings, Applied Mathematics Letters, 24 (2011), 33-38 by A. Rafiq; and give an alternative condition to correct the anomaly.