Noncyclic contractions and relatively nonexpansive mappings in strictly convex fuzzy metric spaces

Gabeleh M., Ekici E., Sen M. D. L.

AIMS MATHEMATICS, vol.7, no.11, pp.20230-20246, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 11
  • Publication Date: 2022
  • Doi Number: 10.3934/math.20221107
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.20230-20246
  • Keywords: strictly convex fuzzy metric space, fuzzy proximal normal structure, best proximity pair, FIXED-POINT THEOREM, MINIMAL SETS
  • Yozgat Bozok University Affiliated: Yes

Abstract

A concept of fuzzy projection operator is introduced and use to investigate the non -emptiness of the fuzzy proximal pairs. We then consider the classes of noncyclic contractions and noncyclic relatively nonexpansive mappings and survey the existence of best proximity pairs for such mappings. In the case that the considered mapping is noncyclic relatively nonexpansive, we need a geometric notion of fuzzy proximal normal structure defined on a nonempty and convex pair in a convex fuzzy metric space. We also prove that every nonempty, compact and convex pair of subsets of a strictly convex fuzzy metric space has the fuzzy proximal normal structure.