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BEST APPROXIMATION TO COMMON FIXED POINTS OF A SEMIGROUP OF NONEXPANSIVE OPERATORS

We study a sequential algorithm for finding the projection of a given point onto the common fixed points set of a semigroup of nonexpansive operators in Hilbert space. The convergence of such an algorithm was previously established only for finitely many nonexpansive operators. Algorithms of this kind have been applied to the best approximation and convex feasibility problems in various fields of applications.