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

Moosa Gabeleh; Elif Uyanık Ekici; Manuel De La Sen; Moosa Gabeleh; Elif Uyanık Ekici; Manuel De La Sen

doi:10.3934/math.20221107

AIMS Mathematics

2022, Volume 7, Issue 11: 20230-20246. doi: 10.3934/math.20221107

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

1.
Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
2.
Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey
3.
Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Bizkaia, Spain

Received: 07 July 2022 Revised: 02 September 2022 Accepted: 02 September 2022 Published: 16 September 2022
MSC : Primary 47H10, 46S50, Secondary 41A65

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.
- strictly convex fuzzy metric space,
- fuzzy proximal normal structure,
- best proximity pair
Citation: Moosa Gabeleh, Elif Uyanık Ekici, Manuel De La Sen. Noncyclic contractions and relatively nonexpansive mappings in strictly convex fuzzy metric spaces[J]. AIMS Mathematics, 2022, 7(11): 20230-20246. doi: 10.3934/math.20221107

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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.

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