Banach Fixed Point Theorem in Extended <i>b</i>_v(<i>s</i>)-Metric Spaces

Abstract

We define the class of extended bv(s)-metric spaces by replacing the real number s≥1 with a strictly increasing continuous function ϕ in the definition of a bv(s)-metric space. Also, we presented an example for this newly introduced space and exhibited that in a particular situation, the class of extended bv(s)-metric spaces reduces to the class of bv(s)-metric spaces. Afterwards, we establish a fixed point theorem which ensured the existence of a fixed point for the self-map satisfying the Banach contractive condition in the context of this newly defined space. Moreover, we compared the proved result with the existing fixed point theorems in the literature.

Keywords

• b-metric space
• rectangular b-metric space
• bv(s)-metric space
• Banach contraction principle