Modified Noor iterations for nonlinear equations in Banach spaces

The purpose of this paper is to analyze the modified three-step iterative scheme for solving nonlinear operator equations in real Banach spaces. Our results can be viewed as an extension of three-step and two-step iterative schemes of Glowinski and Le Tallec [R. Glowinski, P. Le Tallec, Augemented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM Publishing Co., Philadelphia, 1989] Noor [M.A. Noor, Three-step iterative algorithms for multivalued quasi variational inclusions, J. Math. Anal. Appl. 255 (2001) 589-604; M.A. Noor, Some predictor-corrector algorithms for multivalued variational inequalities, J. Optim. Theory Appl. 108 (3) (2001) 659-670; M.A. Noor, T.M. Rassias, Z. Huang, Three-step iterations for nonlinear accretive operator equations, J. Math. Anal. Appl. 274 (2002) 59-68] and Ishikawa [S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974) 147-150].