On Convergence and Stability of the Generalized Noor Iterations for a General Class of Operators

Abstract

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 [5] in a Banach space. As corollaries, some convergence and stability results for the Noor, Ishikawa, Mann and Picard iterative schemes are also established. Our convergence results generalize and extend the results of Berinde [3], Bosede [4], Olaleru [16], Rafiq [21, 22] among others, while our stability results are extensions and generalizations of multitude of results in the literature, including the results of Berinde [1], Bosede and Rhoades [5], Imoru and Olatinwo [9] and Osilike [18].