Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

Year 2023, Volume: 12 Issue: 1, 55 - 64, 30.04.2023

Seyit Temir , Oruç Zincir

https://doi.org/10.54187/jnrs.1254947

Abstract

This paper studies the convergence of fixed points for Garsia-Falset generalized nonexpansive mappings. First, it investigates weak and strong convergence results for Garsia-Falset generalized nonexpansive mappings using the Temir-Korkut iteration in uniformly convex Banach spaces. This paper then exemplifies Garsia-Falset generalized nonexpansive mappings, which exceed the class of Suzuki generalized nonexpansive mappings. Moreover, it numerically compares this iteration's convergence speed with the well-known Thakur iteration of approximating the fixed point of Garsia-Falset generalized nonexpansive mapping. The results show that the Temir-Korkut iteration converges faster than the Thakur iteration converges. Finally, this paper discusses the need for further research.

Keywords

Generalized nonexpansive mapping, Fixed point, Uniformly-convex Banach spaces

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