FIXED POINT RESULTS INVOLVING FUZZY $\eta$-TYPE MAPPINGS WITH APPLICATIONS

In this article, we introduce the notions of fuzzy $\eta$-contraction and fuzzy $\eta$-Suzuki contraction mappings and utilize them to establish fixed point theorems within the broader framework of the Banach contraction principle. These results extend and generalize existing fixed point theorems in the literature. Several corollaries are derived to reinforce the main theorems. Finally, the theoretical findings are applied to demonstrate the existence and uniqueness of solutions for a second-order nonlinear boundary value problem.