WEAK CONVERGENCE THEOREMS FOR FINDING COMMON ELEMENTS OF FINITE SETS IN BANACH SPACES

Abstract

In this paper, we deal with the problem for finding a common element of finite sets in a Banach space. We first prove that an operator given by a convex combination of sunny generalized nonexpansive retractions in a Banach space is asymptotically regular. Using this result, we obtain a weak convergence theorem which is connected with the problem of image recovery. Further, using another weak convergence theorem, we prove a weak convergence theorem of Mann’s type for finding a common element of finite sets in a Banach space.