Fixed Point Theorems for Nonexpansive Type Mappings in Banach Spaces

Pant, Rajendra; Patel, Prashant; Shukla, Rahul; Sen, Manuel De la

doi:10.3390/sym13040585

Cited by 12 publications

(8 citation statements)

References 29 publications

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“…They were able to obtain some fixed point results for their new class of nonexpansive type mappings. R. Pant et al [19] consider the Halpern iteration in 2021 for finding a common fixed point of a nonexpansive type semigroup and a countable family of mappings satisfying condition (E). As a result, the findings in [16,17] have been expanded, generalized, and complemented.…”

Section: Iterative Processesmentioning

confidence: 99%

Convergence and Stability of the Ishikawa Iterative Process for a class of ϕ-quasinonexpansive Mappings

et al. 2022

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The paper analyzes the convergence of Ishikawa iteration to the fixed point of a class of '-quasinonexpansive mappings in uniformly convex Banach spaces, as well as the stability of the Ishikawa iteration used in approximating the fixed point. The work not only confirmed Ishikawa iteration’s convergence and stability to the fixed point of '-quasinonexpansive mappings, but it also pointed the way for future research in the estimate of fixed points of ϕ-quasinonexpansive mappings.

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Section: Iterative Processesmentioning

confidence: 99%

Convergence and Stability of the Ishikawa Iterative Process for a class of ϕ-quasinonexpansive Mappings

et al. 2022

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“…This class of mappings properly contains many important classes of generalized nonexpansive mappings, see Pant et al's [7] study.…”

Section: Introductionmentioning

confidence: 99%

Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems

Shukla,

Panicker

2023

Abstract and Applied Analysis

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This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of α -Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that α -Krasnosel’skiĭ mapping associated with b -enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning b -enriched quasinonexpansive mappings have been proved.

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“…Pant et al established some xed point results for generalized nonexpansive type mappings in Banach spaces (see [16,17,18]).…”

Section: Introductionmentioning

confidence: 99%

Fixed points of $\rho$-nonexpansive mappings using MP iterative process

Panwar

Reena²,

Kumar

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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This research article introduces a new iterative process called MP iteration and proves some convergence and approximation results for the xed points of ρ-nonexpansive mappings in modular function spaces. To demonstrate that MP iterative process converges faster than some well-known existing iterative processes for ρ-nonexpansive mappings, we construct some numerical examples. In the end, the concept of summably almost T-stability for MP iterative process is discussed.

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Fixed Point Theorems for Nonexpansive Type Mappings in Banach Spaces

Abstract: In this paper, we present some fixed point results for a class of nonexpansive type and α-Krasnosel’skiĭ mappings. Moreover, we present some convergence results for one parameter nonexpansive type semigroups. Some non-trivial examples have been presented to illustrate facts.

Cited by 12 publications

References 29 publications

Convergence and Stability of the Ishikawa Iterative Process for a class of ϕ-quasinonexpansive Mappings

Convergence and Stability of the Ishikawa Iterative Process for a class of ϕ-quasinonexpansive Mappings

Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems

Fixed points of $\rho$-nonexpansive mappings using MP iterative process

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