Affiliations: [a] Department of Mathematics, Hajjah University, Hajjah, Yemen
| [b] Department of Mathematics, Aligarh Muslim University, Aligarh, India
| [c] Università degli Studi di Napoli Federico II, Dipartimento di Architettura, Napoli, Italy
Correspondence:
[*]
Corresponding author. Salvatore Sessa, Università degli Studi di Napoli Federico II, Dipartimento di Architettura, Via Toledo 402, 80134 Napoli, Italy. E-mail: sessa@unina.it, salvatore.sessa@alice.it.
Abstract: In this manuscript, we provide a new and novel generalization of the concept of fuzzy contractive mappings due to Gregori and Sapena [Fuzzy Sets and Systems 125 (2002) 245–252] in the setting of relational fuzzy metric spaces. Our findings possibly pave the way for another direction of relation-theoretic as well as fuzzy fixed point theory. We illustrate several examples to show the usefulness of our proven results. Moreover, we define cyclic fuzzy contractive mappings and utilize our main results to prove a fixed point result for such mappings. Finally, we deduce several results including fuzzy metric, order-theoretic and α-admissible results.
Keywords: 47H10, 54H25
Keywords: Fuzzy metric space, fixed point, binary relation, α-admissible
