Czerwik Vector-Valued Metric Space with an Equivalence Relation and Extended Forms of Perov Fixed-Point Theorem

Monairah Alansari, Yahya Almalki and Muhammad Usman Ali ()
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Monairah Alansari: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Yahya Almalki: Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Muhammad Usman Ali: Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad 45550, Pakistan

Mathematics, 2023, vol. 11, issue 16, 1-14

Abstract: In this article, we shall generalize the idea of vector-valued metric space and Perov fixed-point theorem. We shall introduce the notion of Czerwik vector-valued R -metric space by involving an equivalence relation. A few basic concepts and properties related to Czerwik vector-valued R -metric space shall also be discussed that are required to obtain a few extended types of Perov fixed-point theorem.

Keywords: fixed points; vector-valued metric space; Czerwik vector-valued metric space; Czerwik vector-valued ?-metric space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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