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

AbstractLet E be a uniformly smooth Banach space and T : E → E be a continuous and strongly ø-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 Tx = f when T : E → E is ø-strongly accretive. These results generalize the results of Ding [1] into more general ø-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 un = vn = 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