A Theorem on k-Expansive Mapping and its Fixed Point in G𝐽 𝑆 – Metric Space

Objectives: To find a fixed point of k-expansive mapping on GJS-metric space by establishing a theorem on it and to prove the uniqueness of such a fixed point. Methods: A theorem for the k-expansive map on GJS-metric space is established by generalizing an existing contractive condition theorem. Generalization is done by replacing the contractive condition with an expansive type of condition. Findings: Certain conditions that have to be satisfied by a k-expansive mapping for the existence and uniqueness of fixed points in GJS-metric space were found in this article. An example is also given to illustrate the existence of a fixed point. Novelty: GJS-metric space is a new metric space that has been established recently. Furthermore, the fixed point theorem of k-expansive mapping on GJS - metric space has not yet been proved by anyone, and hence it is proved in this article. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: GJS-Metric space; Symmetric GJS-Metric space; GJS-Continuous function; GJS-Cauchy sequence; Expansive mapping; k-Expansive mapping