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Abstract During the last two decades, the problem of constructing iterative techniques for solving different nonlinear problems tackled the ingenuity of many researchers, and has the greatest interest of many of the recent research papers. The main objective of the present thesis is to construct the proofs of many convergence theorems associated with applying the recent iterative techniques to solve the most general nonlinear operator equation of the form A.:\”+ ...t Tx =f in the most general functional spaces. In this research, trials are made to investigate the convergence of the Mann and Ishikawa iterative processes with errors to the unique solution of the general nonlinear operator equation, mentioned before, in Banach space where A, T: X -+ X are Lipschitzian, A is strongly accretive and T is accretive. Furthermore, with some modifications in the proofs of the convergence theorems. fixed point approximations for strongly pseudocontractivc operators arc: also studied. Since the class of ¢-strongly accretive operators is more general than that of accretive operators, then convergence theorems for this class of operators are introduced. Finally, new results concerning T-stability of the Mann and Ishikawa iterations with errors with respect to Lipschitzian mappings in a general complex Banach space have been established |