Fuzzy Θ_f-contractive mappings and their fixed points with applications

Article type: Research Article

Authors: Nasr Saleh, Hayel^{a; b; *} | Imdad, Mohammad^a | Khan, Idrees^c | Hasanuzzaman, Md^a

Affiliations: [a] Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India | [b] Department of Mathematics, Taiz University, Taiz, Yemen | [c] Department of Mathematics, Integral University, Lucknow, India

Correspondence: [*] Corresponding author. Hayel N. Saleh, Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. E-mails: [email protected] and [email protected].

Abstract: In the present article, inspired by the work of Jleli et al. [J. Inequal. Appl. 2014, 38 (2014)] and [J. Inequal. Appl. 2014, 439 (2014)] in metric spaces, we proposed a new class of contractive mappings termed as: fuzzy Θf-contractive mappings by using an auxiliary function Θf : (0, 1) → (0, 1) satisfying suitable properties. This class has further been weakened by defining the class of fuzzy Θf-weak contractive mappings to realize yet another class of contractive mappings. Thereafter, these two newly introduced classes of contractive mappings are utilized to establish some fixed point theorems in M-complete fuzzy metric spaces (in the sense of George and Veeramani). In support of our newly obtained results, we provide some examples besides furnishing applications to dynamic programming.

Keywords: Fixed point, fuzzy Θ_f-contractive mappings, fuzzy Θ_f-weak contractive mappings, fuzzy metric space, dynamic programming

DOI: 10.3233/JIFS-200319

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 5, pp. 7097-7106, 2020