Application of He's homotopy perturbation method for a nonlinear functional equation in Banach spaces.

In the present paper we extend the Homotopy Perturbation Method to find an approximate analytic solution for a nonlinear functional equation in a Banach space. While previously necessary and sufficient conditions were given for the existence of the solution only for the case of a non expansive operator, HPM allowed us to find solutions also for the case of an expansive operator T, as shown in the given example. [ABSTRACT FROM AUTHOR]