Abstract
Suppose K is a closed convex subset of a strictly convex real Banach space E which has a uniformly Gâteaux differentiable norm. Suppose that every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common zero of a family of m -accretive mappings from K to E . As a consequence, an iterative method is constructed to converge to a common fixed point (assuming existence) of a family of pseudocontractive mappings from K to E under certain mild condition.
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