Weak Convergence to a Fixed Point of the Sequence of Mann Type Iterates

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 {xn}∞n=1 defined by xn+1=(1−αn)xn+αnTxn converges weakly to some fixed point of T. A similar result is obtained for continuous generalized nonexpansive mappings.