Iterative solutions of nonlinear equations with φ-strongly accretive operators in uniformly smooth Banach spaces

Abstract

Suppose that X is a uniformly smooth Banach space and T : X → X is a demicontinuous (not necessarily Lipschitz) φ-strongly accretive operator. It is proved that the Ishikawa iterative method with errors converges strongly to the solutions of the equations f = Tx and f = x+ Tx, respectively. A related result deals with the approximation of fixed points of φ-strongly pseudocontractive operators. Our results extend, improve, and unify the recent results obtained by Chidume [1,2] and Zhou [3].