A modified proximal point algorithm for a nearly asymptotically quasi-nonexpansive mapping with an application

Khatoon, Sabiya; Uddin, Izhar; Başarır, Metin

doi:10.1007/s40314-021-01646-9

Cited by 8 publications

(1 citation statement)

References 28 publications

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“…Agwu and Igbokwe [33] worked on a two-step extragradient-viscosity algorithm for the common fixed-point problem of two asymptotically nonexpansive mappings and variational inequality problems in Banach spaces. Khatoon et al [34,35] carried out great work on a modified proximal point algorithm for nearly asymptotically quasi-nonexpansive mappings. Khunpanuk et al [36] worked on a proximal point algorithm for solving common fixed-point problems and convex minimization problems in Geodesic spaces with positive curvature.…”

Section: Lemma 7 ([31]mentioning

confidence: 99%

Approximating Common Solution of Minimization Problems Involving Asymptotically Quasi-Nonexpansive Multivalued Mappings

et al. 2022

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In this paper, an iterative scheme for finding common solutions of the set of fixed points for a pair of asymptotically quasi-nonexpansive mapping and the set of minimizers for the minimization problem is constructed. Using the idea of the jointly demicloseness principle, strong convergence results are achieved without imposing any compactness condition on the space or the operator. Our results improve, extend and generalize many important results in the literature.

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Section: Lemma 7 ([31]mentioning

confidence: 99%

Approximating Common Solution of Minimization Problems Involving Asymptotically Quasi-Nonexpansive Multivalued Mappings

et al. 2022

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A robust alternative to examine data dependency of fixed points of quasi-contractive operators: an efficient approach that relies on the collage theorem

Gürsoy

2024

Comp. Appl. Math.

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Usurelu et al. (Int J Comput Math 98:1049–1068, 2021) presented stability and data dependence results for a TTP (Thakur–Thakur–Postolache) iteration algorithm associated with quasi-strictly contractive mappings and contraction mappings, respectively, but these results were subject to strong conditions on the parametric control sequences used in the TTP iteration algorithm. This article aims to expand those results conducting a thorough analysis of the convergence of TTP and S iteration algorithms and improve those results by removing the restrictions on the parametric control sequences. Additionally, a data dependence result for the TTP iteration algorithm of quasi-strictly contractive mappings is established and several collage theorems are introduced to offer new insights into the data dependence of fixed points of quasi-strictly contractive mappings and to solve related inverse problems. In order to exhibit the dependability and effectiveness of all the results discussed in this work, a multitude of numerical examples are furnished, encompassing both linear and nonlinear differential equations (DEs) and partial differential equations (PDEs). This work can be viewed as an important refinement and complement to the study by Usurelu et al. (Int J Comput Math 98:1049–1068, 2021).

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On the solutions of a nonlinear system of q-difference equations

Turan,

Başarır,

Şahin

2024

Bound Value Probl

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A modified proximal point algorithm for a nearly asymptotically quasi-nonexpansive mapping with an application

Cited by 8 publications

References 28 publications

Approximating Common Solution of Minimization Problems Involving Asymptotically Quasi-Nonexpansive Multivalued Mappings

Approximating Common Solution of Minimization Problems Involving Asymptotically Quasi-Nonexpansive Multivalued Mappings

A robust alternative to examine data dependency of fixed points of quasi-contractive operators: an efficient approach that relies on the collage theorem

On the solutions of a nonlinear system of q-difference equations

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