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In this paper, we establish some strong convergence and stability results of multistep iterative scheme for a general class of operators introduced by Bosede and Rhoades  in a Banach space. As corollaries, some convergence and stability results for the Noor, Ishikawa, Mann and Picard iterative schemes are also established. In the Banach space setting, our convergence results generalize and extend the results of Berinde , Bosede , Olaleru , Rafiq [21, 22] among others, while ourdoi:10.9734/bjmcs/2013/2724 fatcat:tqxqcutiyfehhgepwfgs6noqje