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In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically '-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically '- pseudocontractive mappings in real Banach spaces. Finally, we obtain the convergence theorems of Ishikawa iterative sequence and the modified Ishikawa iterative process with errors.

THE CONVERGENCE THEOREMS FOR COMMON FIXED POINTS OF UNIFORMLY L-LIPSCHITZIAN ASYMPTOTICALLY Φ-PSEUDOCONTRACTIVE MAPPINGS