A quasinonexpansive extension of a mapping with an attractive point in a Hilbert space

TL;DR

This paper introduces a method to extend mappings with attractive points in Hilbert spaces to quasinonexpansive mappings, enabling new convergence theorems for approximating these points.

Contribution

It constructs a quasinonexpansive extension of a mapping with an attractive point, linking fixed points to attractive points in Hilbert spaces.

Findings

Existence of a quasinonexpansive extension under certain conditions

Convergence theorems for generalized hybrid mappings

Extension aligns fixed point set with attractive point set

Abstract

In this paper, we show that, under appropriate conditions, there exists a quasinonexpansive extension of a mapping with an attractive point in the sense of Takahashi and Takeuchi (2011) such that the fixed point set of the extension equals the attractive point set of the given mapping. Then using the quasinonexpansive extension, we establish some convergence theorems for approximating attractive points of a generalized hybrid mapping in the sense of Kocourek, Takahashi, and Yao (2010).