Hyperbolic Valued Metric Space

TL;DR

This paper explores the foundational properties of hyperbolic valued metric spaces, introduces a hyperbolic version of Banach's contraction principle, and constructs a hyperbolic metric on continuous functions, expanding the theoretical framework.

Contribution

It develops basic properties of hyperbolic valued metric spaces and establishes a new contraction principle specific to this setting.

Findings

Established properties of hyperbolic valued metric spaces

Proved a hyperbolic version of Banach's contraction principle

Constructed a hyperbolic valued metric on continuous functions

Abstract

In this paper our main aim is to develop some basic properties of hyperbolic valued metric spaces. We also establish the hyperbolic version of Banach contraction principle. Further we construct a hyperbolic valued metric on the space of all hyperbolic valued continuous functions and prove some results.