S   ∗ p   ‐ b -Partial Metric Spaces with some Results in Common Fixed Point Theorems

A M Zidan

doi:10.1155/2021/5586936

Abstract

In this paper, we introduce the notion of S ∗ P ‐ b -partial metric spaces which is a generalization each of S ‐ b -metric spaces and partial-metric space. Also, we study and prove some topological properties, to know the convergence of the sequences and Cauchy sequence. Finally, we study a new common fixed point theorem in these spaces.

Highlights

There are a large number of generalizations of the Banach contraction principle with different use forms of contractual terms in a variety of generalized metric spaces
Let ðY, ≼Þ be a partially ordered set, f and g be weakly increasing self-mapping on a complete S∗bP -metric space with ζ ≥ 1
Of the following two cases, assume that one of the following cases is satisfied: (a) if a nondecreasing sequence fwng converges to r ∈ Y implies fwng≼r for all n ∈ N

Summary

Introduction

There are a large number of generalizations of the Banach contraction principle with different use forms of contractual terms in a variety of generalized metric spaces. A function D∗ : Y × Y × Y ⟶ 1⁄20,∞Þ is said to be a D∗ -metric spaces on a nonempty set Y, if for all w, t, r ∈ Y, the following conditions hold: (D∗1 ) D∗ðw, t, rÞ ≥ 0 ((DD∗2∗3 ))

Results

Conclusion