The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous \(\varphi \)-strongly accretive operators in uniformly smooth Banach spaces (Q884177)

In order to approximate fixed points of self-mappings in normed linear spaces, several methods have been introduced so far in order to remove difficulties when trying to apply Picard iteration (also known as the method of successive approximations). Among these methods, one can find Mann and Ishikawa iterations and their versions with errors. In the present paper, the authors establish the equivalence between the convergence of Mann iteration with errors and the Ishikawa iteration with errors in the class of demicontinuous \(\Phi\)-strongly accretive operators in uniformly smooth Banach spaces (Theorem 2.1). Some examples to illustrate the merit of their result in comparison to the case of usual strongly accretive mappings are also given.