GENERALIZED φ-FIXED POINT RESULTS FOR NONLINEAR MAPPINGS WITH AN APPLICATION TO FRACTIONAL DIFFERENTIAL EQUATIONS

In the present work, we investigate the existence and uniqueness of φ-fixed points and common φ-fixed points for a class of nonlinear mappings defined on metric spaces. The results are obtained under a unified admissibility framework that encompasses several generalized admissibility notions. The contractive conditions are formulated by employing C-class functions together with altering distance functions. The established theorems extend and improve various existing results in the literature. To illustrate the applicability of the theoretical findings, appropriate examples are provided. Furthermore, as an application of the main results, the existence of solutions for a class of fractional differential equations is discussed.