Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

• Published in: Journal of New Results in Science
• Main Authors: Oruç Zincir, Seyit Temir
• Format: Article
• Language: English
• Published: Tokat Gaziosmanpasa University 2023-04-01
• Subjects: generalized nonexpansive mapping; fixed point; uniformly-convex banach spaces
• Online Access: https://dergipark.org.tr/en/download/article-file/2968108

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.