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:
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Corresponding author. Hayel N. Saleh, Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. E-mails: hnsaleh112@myamu.ac.in and nasrhayel@gmail.com.
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.
