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

AIMS Mathematics

article

Moosa Gabeleh¹  Elif Uyanık Ekici²  Manuel De La Sen³ 

[1] Department of Mathematics, Ayatollah Boroujerdi University;Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University;Institute of Research and Development of Processes, University of the Basque Country

关键词: strictly convex fuzzy metric space;    fuzzy proximal normal structure;    best proximity pair;   

DOI  :  10.3934/math.20221107

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY