Remarks on b-enriched nonexpansive mappings

TL;DR

This paper critically examines the concept of enriched nonexpansive mappings, revealing that it essentially coincides with the well-known nonexpansive mappings, and emphasizes the need for further clarification in the literature.

Contribution

The paper demonstrates that the concept of enriched nonexpansive mappings is redundant, urging a reconsideration and clearer definition within metric-fixed point theory.

Findings

Enriched nonexpansive mappings are equivalent to nonexpansive mappings.

The concept needs reconsideration due to redundancy.

Highlights gaps and ambiguities in existing literature.

Abstract

In this note, we analyzed the concept of enriched nonexpansive which was proposed in "Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces" (Carpathian J. Math., 35(2019), No. 3, 293-304.) Through our analysis, we conclude that the idea of enriched nonexpansive needs reconsideration, as it coincides with well known concept of nonexpansive. Our findings provide an insights into the existing literature and highlight the need for further investigations and clarifications in the existing literature on a metric-fixed point theory.