Abstract

Let T be a quasi-nonexpansive self-mapping of a closed convex subset of a uniformly convex Banach space satisfying Opial′s condition with I- T demiclosed with respect to zero. Then the sequence { x n } ∞ n=1 defined by x n+1 =(1−α n ) x n +α nTx n converges weakly to some fixed point of T. A similar result is obtained for continuous generalized nonexpansive mappings.

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