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Hyperbolic Valued Metric Space

Chinmay Ghosh, Anirban Bandyopadhyay, Soumen Mondal

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.

Hyperbolic Valued Metric Space

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.

Paper Structure

This paper contains 4 sections, 18 theorems, 70 equations.

Table of Contents

  1. Introductions and Preliminaries
  2. Basic definitions and lemmas
  3. Main results
  4. Examples

Key Result

Lemma 5

A sequence $\{x_{n}\}$ in a $\mathbb{D}$-metric space $(X,d_{\mathbb{D}})$ converges to $\alpha$ if and only if $\lim\limits_{n\rightarrow \infty }d_{\mathbb{D}}(x_{n},\alpha )=0.$

Theorems & Definitions (42)

  • Definition 1: $ku$
  • Definition 2
  • Definition 3
  • Definition 4: $sai$
  • Lemma 5
  • Definition 6
  • Lemma 7
  • Definition 8: $sai$
  • Remark 9
  • Definition 10: $sai$
  • ...and 32 more