A Necessary and Sufficient Condition for the Convergence of a Sequence of Iterates for Quasi-nonexpansive Mappings


Introduction. The purpose of this note is to present two theorems which provide necessary and sufficient conditions for the convergence of the successive approximation method (Theorem 1) and of the convex combination iteration method (Theorem 2) for quasi-nonexpansive mappings defined on suitable subsets of Banach spaces and with nonempty sets of fixed… (More)


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