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

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 ℛ-metric space