Existence and convergence theorems for Berinde nonexpansive multivalued mapping on Banach spaces

Bunlue, Nuttawut; Suantai, Suthep

doi:10.1007/s13370-019-00661-8

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…Moreover, we also prove strong and ∆−convergence theorems of the Ishikawa iteration process for the class of Gquasinonexpansive mappings which includes the class of Osilike-Berinde-G-nonexpansive mappings as well. Our results extend and improve the results in [6,17,28,31,35] and many others.…”

Section: Introductionsupporting

confidence: 91%

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Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs

Kaewkhao¹,

Klangpraphan²,

Panyanak³

2021

CJM

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"In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show that every Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping. We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and \Delta-convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed."

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Section: Introductionsupporting

confidence: 91%

“…In 2019, Bunlue and Suantai [6] proved the existence of fixed points as well as the demiclosed principle for Osilike-Berinde-nonexpansive mappings in Banach spaces satisfying the Opial's condition. It was quickly noted by Klangpraphan and Panyanak [17] that the results in [6] can be extended to complete CAT(0) spaces.…”

Section: Introductionmentioning

confidence: 99%

Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs

Kaewkhao¹,

Klangpraphan²,

Panyanak³

2021

CJM

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“…Furthermore, many authors approximated common fixed points and proved existence and convergence results for multivalued Berinde nonexpansive mappings (1.1) in linear spaces, e.g. [5,6].…”

Section: Introductionmentioning

confidence: 99%

Existence and estimation of the fixed points of enriched Berinde nonexpansive mappings

Ali¹,

Jubair²

2023

MMN

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In this article, inspired by Berinde (Approximating fixed points of enriched nonexpansive mappings by Krasnoselskii iteration in Hilbert spaces, Carpathian J. Math. 35(3), 2019, 293-304), we define and study a new enriched class of mappings which includes many other contractive type mappings. We prove an existence result for the fixed point of newly introduced mapping. We also estimate fixed points of the proposed mapping via newly modified Mann iteration. In the process, some convergence results are also obtained for the proposed class of mappings in Uniformly convex Banach space.

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“…More works regarding both contractive and nonexpansive mappings can be found in [6,7,8,11,12,21] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence of fixed points of weak enriched nonexpansive mappings in Banach spaces

Suantai

Chumpungam

Sarnmeta

2021

CJM

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In this work, we introduce and study a new class of weak enriched nonexpasive mappings which is a generalization of enriched nonexpansive mappings provided by Berinde [Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces], Carpathian J. Math., 35 (2019), No. 3, 293–304]. This class of mappings generalizes several important classes of nonlinear mappings. We prove some fixed point theorems regarding this kind of mappings which extend some important results in [Berinde, V., Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35 (2019), No. 3, 293–304]. Moreover, some examples, to ensure the existence of these mappings and support our main theorems, are also given.

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Existence and convergence theorems for Berinde nonexpansive multivalued mapping on Banach spaces

Cited by 4 publications

References 16 publications

Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs

Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs

Existence and estimation of the fixed points of enriched Berinde nonexpansive mappings

Existence of fixed points of weak enriched nonexpansive mappings in Banach spaces

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