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

2022/02/03 by Koji Aoyama, Aoyama, Koji
Computer Science · Mathematics · #Fixed Point Theorems Analysis #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #math.FA

paper · pdf · doi:10.48550/arxiv.2202.01419

arxiv created 2022/02/03 · arxiv updated 2022/02/04

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).

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