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, cilt.8, sa.2, ss.284-304, 2025 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.31838/rna/2025.08.02.022
  • Dergi Adı: Results in Nonlinear Analysis
  • Derginin Tarandığı İndeksler: Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.284-304
  • Anahtar Kelimeler: b − interval metric, completeness, Continuity, convergence, null set, T0 − topology
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

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.