Partial b_{v}(s) and b_{v}({\theta}) metric spaces and related fixed point theorems

TL;DR

This paper introduces two new generalized metric spaces, partial b_{v}(s) and b_{v}({ heta}), extending many existing spaces, and proves fixed point theorems within these frameworks, supported by numerical examples.

Contribution

The paper defines novel partial b_{v}(s) and b_{v}({ heta}) metric spaces and establishes fixed point theorems in these spaces, broadening the scope of metric space theory.

Findings

Fixed point theorems proven in new spaces

Definitions of partial v-generalized metric spaces

Numerical examples supporting the new concepts

Abstract

In this paper, we introduced two new generalized metric spaces called partial b_{v}(s) and b_{v}({\theta}) metric spaces which extend b_{v}(s) metric space, b-metric space, rectangular metric space, v-generalized metric space, partial metric space, partial b-metric space, partial rectangular b-metric space and so on. We proved some famous theorems such as Banach, Kannan and Reich fixed point theorems in these spaces. Also, we give definition of partial v-generalized metric space and show that these fixed point theorems are valid in this space. We also give numerical examples to support our definitions. Our results generalize several corresponding results in literature.