Investigation of near fixed points, near fixed interval ellipse and its equivalence classes
Results in Nonlinear Analysis, vol.8, no.2, pp.284-304, 2025 (Scopus)
- 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.