Application of Perove Type Fixed Point Theorem in Vector Valued $B$-Metric Spaces

Abstract

In this paper, we extended the definition of \( b \)-metric spaces to encompass the vectorial scenario, wherein the distance is represented as a vector, and the constant in the triangle inequality axiom is substituted with a matrix. For these spaces, we present findings that are similar to those in the \( b \)-metric framework: fixed-point theorems, stability results, and a version of Ekeland's variational principle. Consequently, we also obtain a variation of Caristi's fixed-point theorem.