Approximating fixed points of Suzuki-generalized nonexpansive mappings

Phuengrattana, Withun

doi:10.1016/j.nahs.2010.12.006

Cited by 29 publications

(26 citation statements)

References 20 publications

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“…Suzuki [21] obtained fixed point theorems and convergence theorems for Suzuki generalized nonexpansive mappings. In 2011, Phuengrattana [14] proved convergence theorems for Suzuki generalized nonexpansive mappings using the Ishikawa iteration in uniformly convex Banach spaces and CAT(0) spaces. Recently, fixed point theorems for Suzuki generalized nonexpansive mappings have been studied by a number of authors see e.g.…”

Section: Preliminariesmentioning

confidence: 99%

Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process

Ullah

Arshad

2018

Filomat

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In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Numerical example is given to show the efficiency of new iteration process. Our results are the extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.

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Section: Preliminariesmentioning

confidence: 99%

Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process

Ullah

Arshad

2018

Filomat

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“…In 2011, Phuengrattana [15] proved convergence theorems for mappings satisfying condition (C) using the Ishikawa iteration in uniformly convex Banach spaces. Recently, fixed point theorems for Suzuki's generalized non expansive mappings and nonlinear mappings have been studied by a large number of researchers, e.g.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Fixed Points for Suzuki's Generalized Non-Expansive Mappings

Ali¹,

Ali²,

Kumar³

2019

Preprint

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In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

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“…It follows that CAT(0) spaces have a convex structure W (x, y, λ) := λx ⊕ (1 − λ)y. Existence theorems and convergence theorems in convex metric spaces and CAT(0) spaces have been studied and investigated, see, for examples, [13,5,16,12,18,15,19,1,2]. The notion of the asymptotic center can be introduced in the general setting of a CAT(0) space X as follows: Let {x n } be a bounded sequence in X.…”

Section: Preliminariesmentioning

confidence: 99%