Nonlinear equations of the φ-strongly pseudocontractive type in arbitrary Banach spaces

Suppose E is an arbitrary real Banach space and K is a nonempty closed convex and bounded subset of E. Suppose T : K --> K is a uniformly continuous phi-strong pseudocontraction. It is proved that if T has a fixed point, then both the Mann and the Ishikawa iteration methods converge strongly to the fixed point of T. Furthermore, our results also hold for the slightly more general class of phi-hemicontractive maps. Related results deal with the iterative approximation of solutions of phi-strongly accretive operator equations in arbitrary Banach spaces.