Iterative approximation of fixed points of contraction mappings in complex valued Banach spaces

We approximate the fixed points of contraction mappings using the Picard–Krasnoselskii hybrid iterative process, which is known to converge faster than all of Picard, Mann and Ishikawa iterations in complex valued Banach spaces. Moreover, we prove analytically and with a numerical example that the Picard–Mann hybrid iteration and the Picard–Krasnoselskii hybrid iteration have the same rate of convergence. Furthermore, we apply our results in finding solutions of delay differential equations in complex valued Banach spaces.