Generalized enriched cyclic contractions with application to generalized iterated function system

Abbas, Mujahid; Anjum, Rizwan; Iqbal, Hira

doi:10.1016/j.chaos.2021.111591

Cited by 18 publications

(7 citation statements)

References 30 publications

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“…The above Theorem 3 has been studied and generalized by many researchers (see [17][18][19][20][21]). Theorem 3 is generalized by Abbas et al [4] in 2022 as follows: Theorem 4 ([4]).…”

Section: Remarkmentioning

confidence: 99%

Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions

Anjum,

Fulga,

Akram

2023

Mathematics

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The aim of this paper is manifold. We first define the new class of operators called MR-Kannan interpolative type contractions, which includes the Kannan, enriched Kannan, interpolative Kannan type, and enriched interpolative Kannan type operators. Secondly, we prove the existence of a unique fixed point for this class of operators. Thirdly, we study Ulam-Hyers stability, well-posedness, and periodic point properties. Finally, an application of the main results to the variational inequality problem is given.

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“…The above Theorem 3 has been studied and generalized by many researchers (see [17][18][19][20][21]). Theorem 3 is generalized by Abbas et al [4] in 2022 as follows: Theorem 4 ([4]).…”

Section: Remarkmentioning

confidence: 99%

Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions

Anjum,

Fulga,

Akram

2023

Mathematics

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“…In the recent years, a number of papers have appeared in the literature dealing with the fixed point theorems for enriched nonexpansive type mappings [9][10][11]. It was proven that any enriched contraction mapping defined on a Banach space has a unique fixed point, which can be approximated by means of the Krasnoselskij iterative scheme.…”

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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“…This observation suggested that one could enrich the classes of contractive mappings studied in the framework of metric spaces by imposing certain contractive condition on T λ instead of T itself. Employing this approach, the classes such as enriched contractions and enriched φ-contractions [11], enriched Kannan contractions [12], enriched Chatterjea mappings [14], enriched nonexpansive mappings in Hilbert spaces [13], enriched multivalued contractions [3] and enriched Ćirić-Reich-Rus contraction [15], enriched cyclic contraction [5], enriched modified Kannan pair [2], enriched quasi contraction [4] were introduced and studied. Abbas et al [3] proved fixed point results by imposing the condition that T λorbital subset is a complete subset of a normed space (see, Theorem 3 of [3]).…”

Section: Karapinar Introduced a New Class Of Kannan Type Operators Ca...mentioning

confidence: 99%

“…On the other hand, authors [2,3,4,7,12,13,14,15,16,17] used the technique of enrichment of contractive mappings in the setting of Banach spaces.…”

Section: Introductionmentioning

confidence: 99%

Fixed point results of enriched interpolative Kannan type operators with applications

Abbas

Anjum²,

Riasat³

2022

Appl. Gen. Topol.

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The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains theclasses of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskij iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problems is solved.

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Generalized enriched cyclic contractions with application to generalized iterated function system

Cited by 18 publications

References 30 publications

Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions

Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions

Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems

Fixed point results of enriched interpolative Kannan type operators with applications

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