Approximating fixed points of Φ-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces

Abstract Let E be a uniformly smooth Banach space and T : E → E be a continuous and strongly o-hemicontractive mapping. This paper proves that, under suitable conditions, the Ishikawa iterative sequence with errors strongly converges to the unique fixed point of T . The related result deals with the strong convergence of the Ishikawa iterative sequence with errors to the unique solution of the equation T x = f when T : E → E is o-strongly accretive. These results generalize the results of Ding [1] into more general o-hemicontractive operators and extend a recent paper written by Osilike [2] in two ways. 1. (i) The Lipschitzian continuity is replaced by the continuity on mapping T . 2. (ii) If the errors u n = v n = 0, for all n ∈ N , our theorems of this paper extend results of Osilike [2] to the more general class of real uniformly smooth Banach spaces .