Enriched Multivalued Contractions with Applications to Differential Inclusions and Dynamic Programming

Abbas, Mujahid; Anjum, Rizwan; Berinde, Vasile

doi:10.3390/sym13081350

Cited by 19 publications

(13 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(c) the results in [11] from the class of enriched multivalued nems to the class of enriched Suzuki generalized multivalued n-expansive mappings Hence, the results obtained in this paper extend, improve and generalize several well known results currently in literature. Data Availability No data were used to support this study.…”

Section: Discussionsupporting

confidence: 81%

See 1 more Smart Citation

Approximating Fixed Points for Enriched Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces

Agwu

Saleem²,

Ishtiaq³

et al. 2022

Preprint

View full text Add to dashboard Cite

In this manuscript, we establish a novel class of nonlinear mappings called β-enriched Suzuki generalized multivalued non-expansive mappings and prove a new existence of common fixed points for a commuting pair comprising an enriched single-valued and an enriched multivalued mapping both satisfying condition (C) in the setup of a uniformly convex Banach space. Further, weak and strong convergence results are obtained for an infinite family of this new class of mappings in the framework of uniformly convex Banach spaces. A nontrivial numerical example is presented to validate the main results of this paper. Our results extend, improve and generalize many well known results currently in literature.

show abstract

Section: Discussionsupporting

confidence: 81%

“…It is shown in [11] that Γ is an (1, 1)-enriched multivalued contraction but not a contraction in the sense of Nadler [8].…”

Section: Example 14 ([26]mentioning

confidence: 99%

Approximating Fixed Points for Enriched Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces

Agwu

Saleem²,

Ishtiaq³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…where k ∈ [0, ∞) and θ ∈ [0, k). For more results on enriched type contraction, the reader may see [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Rectangular Gb-Metric Spaces and Some Fixed Point Theorems

Cui

2022

Axioms

View full text Add to dashboard Cite

In this paper, we first introduce the concept of rectangular Gb-metric space which generalizes the notion of rectangular metric space and Gb-metric space. Then, some fixed point results connected with certain contractions are obtained in the setting of rectangular Gb-metric spaces. Additionally, we also introduce the concept of convex rectangular Gb-metric space by means of the convex structure and study the fixed points of enriched type contractions in this space.

show abstract

“…Abbas et al [3] proved fixed point results by imposing the condition that T λ -orbital subset is a complete subset of a normed space (see, Theorem 3 of [3]). Similarly, Górnicki and Bisht [24] considered the enriched Ćirić-Reich-Rus contraction operators and proved a fixed point theorem by imposing the condition that T λ is asymptotically regular mapping (see, Theorem 3.1 of [24]).…”

Section: Introductionmentioning

confidence: 99%

Fixed point results of enriched interpolative Kannan type operators with applications

Abbas

Anjum²,

Riasat³

2022

Appl. Gen. Topol.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Enriched Multivalued Contractions with Applications to Differential Inclusions and Dynamic Programming

Cited by 19 publications

References 33 publications

Approximating Fixed Points for Enriched Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces

Approximating Fixed Points for Enriched Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces

Rectangular Gb-Metric Spaces and Some Fixed Point Theorems

Fixed point results of enriched interpolative Kannan type operators with applications

Contact Info

Product

Resources

About