Weak and strong convergence theorems for three Suzuki’s generalized nonexpansive mappings

Temir, Seyit

doi:10.2298/pim2124121t

Cited by 2 publications

(1 citation statement)

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“…Such mappings were referred to as belonging to the class of mappings satisfying condition (C) (also referred as Suzuki GNM), which properly includes the class of nonexpansive mappings. Recently, fixed point theorems for Suzuki generalized nonexpansive mappings have been studied by a number of authors [10][11][12][13][14]. Every self-mapping Ψ on K providing condition (C) has an almost fixed point sequence for a nonempty bounded and convex subset K. Two new classes of GNMs that are wider than those providing the condition (C) were presented in 2011 by Garsia-Falset et al [2], while retaining their fixed point properties.…”

Section: Introductionmentioning

confidence: 99%

Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

Temir

ZİNCİR

2023

Journal of New Results in Science

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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.

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Section: Introductionmentioning

confidence: 99%

Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

Temir

ZİNCİR

2023

Journal of New Results in Science

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APPROXIMATING OF FIXED POINTS FOR MULTI-VALUED GENERALIZED a-NONEXPANSIVE MAPPINGS IN BANACH SPACES

Temir

2023

AnnalsARSciMath

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In this paper, we study multi-valued generalized anonexpansive mappings in uniformly convex Banach spaces. We introduce a new multi-valued iterative process and prove some weak and strong convergence results in uniformly convex Banach space. We also study the stability of this iteration process. Further, we provide a numerical example of the multi-valued generalized a-nonexpansive mapping. Finally, the convergence of this iteration process to the fixed point for multi-valued generalized a-nonexpansive mapping is discussed on this numerical example.

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Weak and strong convergence theorems for three Suzuki’s generalized nonexpansive mappings

Cited by 2 publications

References 10 publications

Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

Approximating of fixed points for Garsia-Falset generalized nonexpansive mappings

APPROXIMATING OF FIXED POINTS FOR MULTI-VALUED GENERALIZED a-NONEXPANSIVE MAPPINGS IN BANACH SPACES

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