Existence of fixed points for generalized α-admissible Geraghty and application to solution of nonlinear differential equations

Recently, samet et al. introduced an interesting extension of the Banach contraction principle. In this paper, motivated by the main idea of Samet et al., we introduce the concept of α-admissible α-θ-generalized mappings in metric spaces and give and prove several theorems of the existence and uniqueness of a fixed point in complete metric spaces for such mappings. The results obtained in this study, generalize many of the results in this field, especially, the results presented by Jleli et al. and the work done by Geraghty. By presenting an example, we show that our results are real generalization of the previous results. Next, we get new results in ordered metric spaces and graphical metric spaces using the concept of α-admissible α-θ-generalized mappings. Finally, we present an application of our obtained results for the existence and uniqueness of the solution of nonlinear first-order ordinal differential equations and periodic boundary value problems.