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Search Results (4)

Search Parameters:
Keywords = enriched φ-contraction

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16 pages, 338 KiB  
Article
Existence and Approximation of Fixed Points of Enriched φ-Contractions in Banach Spaces
by Vasile Berinde, Jackie Harjani and Kishin Sadarangani
Mathematics 2022, 10(21), 4138; https://doi.org/10.3390/math10214138 - 5 Nov 2022
Cited by 1 | Viewed by 1433
Abstract
We introduce the class of enriched φ-contractions in Banach spaces as a natural generalization of φ-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of [...] Read more.
We introduce the class of enriched φ-contractions in Banach spaces as a natural generalization of φ-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results by studying the existence and uniqueness of the solutions of some second order (p,q)-difference equations with integral boundary value conditions. Full article
(This article belongs to the Special Issue Research Trends and Challenges in the Theory of Nonlinear Analysis and Its Applications)
11 pages, 307 KiB  
Article
φ-ψ-Contractions under W-Distances Employing Symmetric Locally T-Transitive Binary Relation
by Mohammad Arif, Mohammad Imdad and Salvatore Sessa
Symmetry 2022, 14(7), 1456; https://doi.org/10.3390/sym14071456 - 16 Jul 2022
Cited by 1 | Viewed by 1051
Abstract
The intent of this paper is to prove the relation-theoretic fixed point results under φ-ψ-contractions involving W-distance on a metric space and equipped with a symmetric locally T-transitive binary relation (not necessarily transitive relation). Our results enrich and [...] Read more.
The intent of this paper is to prove the relation-theoretic fixed point results under φ-ψ-contractions involving W-distance on a metric space and equipped with a symmetric locally T-transitive binary relation (not necessarily transitive relation). Our results enrich and improve several fixed point results of the existing literature. Full article
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points)
15 pages, 319 KiB  
Article
Existence and Approximation of Fixed Points of Enriched Contractions and Enriched φ-Contractions
by Vasile Berinde and Mădălina Păcurar
Symmetry 2021, 13(3), 498; https://doi.org/10.3390/sym13030498 - 18 Mar 2021
Cited by 19 | Viewed by 2874
Abstract
We obtain existence and uniqueness fixed point theorems as well as approximation results for some classes of mappings defined by symmetric contractive type conditions in a convex metric space in the sense of Takahashi. By using a new approach, i.e., the technique of [...] Read more.
We obtain existence and uniqueness fixed point theorems as well as approximation results for some classes of mappings defined by symmetric contractive type conditions in a convex metric space in the sense of Takahashi. By using a new approach, i.e., the technique of enrichment of contractive type mappings, we obtain general results which extend the well known Banach contraction mapping principle from metric spaces as well as other corresponding results for enriched mappings defined on Banach spaces. To indicate the relevance of our new results, we present some important particular cases and future directions of research. Full article
12 pages, 303 KiB  
Article
On Recent Results Concerning F-Contraction in Generalized Metric Spaces
by Jelena Vujaković, Slobodanka Mitrović, Mirjana Pavlović and Stojan Radenović
Mathematics 2020, 8(5), 767; https://doi.org/10.3390/math8050767 - 11 May 2020
Cited by 17 | Viewed by 2208
Abstract
In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce ( φ , F ) -weak contraction and establish the corresponding fixed point result. Using [...] Read more.
In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce ( φ , F ) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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