Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

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Journal of New Results in Science
Volume:12 Issue:1
Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

Authors : Seyit TEMİR, Oruç ZİNCİR

Pages : 55-64

Doi:10.54187/jnrs.1254947

View : 50 | Download : 13

Publication Date : 2023-04-30

Article Type : Research Paper

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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