Investigation of near fixed points, near fixed interval ellipse and its equivalence classes

Joshi M., Tomar A., Zubair S. T., Mukheimer A., Abdeljawad T.

Results in Nonlinear Analysis, vol.8, no.2, pp.284-304, 2025 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.31838/rna/2025.08.02.022
  • Journal Name: Results in Nonlinear Analysis
  • Journal Indexes: Scopus, Directory of Open Access Journals
  • Page Numbers: pp.284-304
  • Keywords: b − interval metric, completeness, Continuity, convergence, null set, T0 − topology
  • Istanbul Gelisim University Affiliated: Yes

Abstract

The objective of the manuscript is to employ the Hardy-Roger contraction to determine the near fixed point and its unique equivalence class in the context of the b − interval metric space. Further, an improved b − interval metric variant of a quasi-contraction characterizing the completeness of a b − interval metric space is exhibited. Various illustrations have been provided to show the existence of a near fixed point and its distinct equivalence class for both continuous and discontinuous maps developed in the b − interval metric space. As an application of the b − interval metric, a near-fixed interval ellipse and its unique equivalence ε −class are introduced to study the geometry of non-unique nearfixed points.