Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric

Baranwal H., Bisht R. K., Chand A. K. B., Yao J.

MATHEMATICS, vol.12, no.18, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 18
  • Publication Date: 2024
  • Doi Number: 10.3390/math12182877
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

This paper explores fixed points for both contractive and non-contractive mappings in traditional b-metric spaces, preordered b-metric spaces, and random b-metric spaces. Our findings provide insights into the behavior of mappings under various constraints and extend our approach to include coincidence and common fixed-point theorems in these spaces. We present new examples and graphical representations for the first time, offering novel results and enhancing several related findings in the literature, while broadening the scope of earlier works of Ran and Reurings, Nieto and Rodriguez-Lopez, Gornicki, and others.