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

We prove the existence of a unique xed point for a mapping satisfying a rational typecontractive inequality condition in complex-valued Banach spaces. We approximate this xedpoint via some xed point iterative processes with high rate of convergence. We then provethat our results are valid in cone metric spaces with Banach algebras. Furthermore, our resultsare applied in nding the solutions of delay dierential equations. Our results extend andgeneralize several known results in the literature