Iterative process with errors to locally strictly pseudocontractive maps in Banach spaces

Let K be a nonempty subset of a uniformly smooth Banach space X and A : K → X be a locally strickly pseudocontractive map with bounded range. The Mann and Ishikawa iterative sequences with errors, which strongly converge to the unique fixed point of A are given under weaker conditions. These results answer positively the open problems mentioned by Deng and Ding [1, p. 122] and Chidume [2, p. 550]. The related results deal with the problems that the Mann and Ishikawa iterative sequences with errors strongly converge to the unique solution of the equation Tx = f when T : X → X is locally strongly accretive such that the range of I – T is bounded.