APPROXIMATIONS OF THE ITERATIVE SEQUENCES FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES

APPROXIMATIONS OF THE ITERATIVE SEQUENCES FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES

In this paper, we first introduce some iterative sequences of Halpern type for asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces and then we discuss strong convergence for the iterative processes. The results presented in this paper extend, supplement and improve the correspoding main results of Reich [11], Shimizu and Takahashi [13], Shioji and Takahashi [15], [16] and Wittmann [18].

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