Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation

Fahim Ud Din, Muhammad Din, Umar Ishtiaq () and Salvatore Sessa ()
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Fahim Ud Din: Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
Muhammad Din: Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
Umar Ishtiaq: Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54782, Pakistan
Salvatore Sessa: Dipartimento di Architettura, Università Dinapoli Federico II, Via Toledo 403, 80121 Napoli, Italy

Mathematics, 2023, vol. 11, issue 1, 1-18

Abstract: The purpose of this article is to discuss some new aspects of the vector-valued metric space. The idea of an arbitrary binary relation along with the well-known F contraction is used to demonstrate the existence of fixed points in the context of a complete vector-valued metric space for both single- and multi-valued mappings. Utilizing the idea of binary relation, and with the help of F contraction, this work extends and complements some of the very recently established Perov-type fixed-point results in the literature. Furthermore, this work includes examples to justify the validity of the given results. During the discussion, it was found that some of the renowned metrical results proven by several authors using different binary relations, such as partial order, pre-order, transitive relation, tolerance, strict order and symmetric closure, can be weakened by using an arbitrary binary relation.

Keywords: Perov fixed point; ordered theoretic Perov fixed point; ? contraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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