Fixed point results for a new mapping related to mean nonexpansive mappings

2016/09/22 by Torrey M. Gallagher, Gallagher, Torrey M.
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1609.07163

openalex publication_date 2016/09/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Mean nonexpansive mappings were first introduced in 2007 by Goebel and Japon Pineda and advances have been made by several authors toward understanding their fixed point properties in various contexts. For any given (α₁, α₂)-nonexpansive mapping T of a Banach space, many of the positive results have been derived from properties of the mapping T_α= α₁ T + α₂T²= (α₁I + α₂T)∘ T which is nonexpansive. However, the related mapping T ∘ (α₁I + α₂T) has not yet been studied. In this paper, we investigate some fixed point properties of this new mapping and discuss relationships between (α₁I + α₂T)∘ T and T∘(α₁I + α₂T).

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