Some Strong Convergence Results for Mann and Ishikawa Iterative Processes in Banach Spaces (dedicated in Occasion of the 70-years of Professor

In this paper, we establish some strong convergence results for Mann and Ishikawa iterative processes in a Banach space setting by employing some general contractive conditions as well as weakening further the conditions on the parameter sequence { n} ⊂ [0, 1]. In addition, in some of our results, we introduce some innovative ideas which make our results distinct from some previous ones. In particular, our results generalize, extend and improve those of [V. Berinde; On the convergence of Mann iteration for a class of quasicontractive operators, Preprint, North University of Baia Mare (2003)] and [V. Berinde; On the Convergence of the Ishikawa Iteration in the Class of Quasi-contractive Operators, Acta Math. Univ. Comenianae Vol. LXXIII (1) (2004), 119-126] as well as some other analogous results in the literature.