Existence and approximation of fixed point of a nonlinear mapping satisfying rational type contractive inequality condition in complex-valued Banach spaces

Abstract

We prove the existence of a unique fixed point for a mapping satisfying a rational type contractive inequality condition in complex-valued Banach spaces. We approximate this fixed point via some fixed point iterative processes with high rate of convergence. We then prove that our results are valid in cone metric spaces with Banach algebras. Furthermore, our results are applied in finding the solutions of delay differential equations. Our results extend and generalize several known results in the literature.