Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equations

This paper introduces the concept of $(P,\psi )$ -type almost contractive conditions for fuzzy mappings in b-metric spaces. This novel framework is employed to establish certain fuzzy fixed point results in complete b-metric spaces. An illustrative example is provided to validate the assumptions of the main theorem, ensuring the existence of fuzzy fixed points. Furthermore, the existence of a solution to a second-order nonlinear boundary value problem is demonstrated by transforming the problem into a fixed point equation and applying the proven results. Several corollaries are derived as consequences of the main findings. The results presented in this work extend and generalize numerous existing fixed point theorems in the literature.