Interpolative best proximity point results via γ contraction with applications

SANGURLU SEZEN M.

AIMS Mathematics, vol.10, no.1, pp.1350-1366, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.3934/math.2025062
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.1350-1366
  • Keywords: fuzzy metric space, interpolative proximal fuzzy contraction, ordered fuzzy metric space
  • Gazi University Affiliated: Yes

Abstract

In this paper, we introduce a ρ interpolative Kannan and Ćirić Reich Rus type fuzzy proximal contraction using a Ύ contraction. We prove some best proximity theorems of this new approximation using the concept of ρ proximal admissibility in complete fuzzy metric spaces. We generalize some previous studies and present fixed point results of the best proximity theorems in complete fuzzy metric spaces. Also, we extend some best proximity results to the partially ordered fuzzy metric spaces.