Shrinking Projection Methods for Maximal Monotone Operators and Quasi-nonexpansive Mappings

In this paper, we consider a new shrinking projection method for finding common elements of the set of fixed points of a quasi-φ-nonexpansive mapping and the set of zero points of a maximal monotone operator. We establish a strong convergence theorem of common elements by using new analysis techniques in the setting of reflexive, strictly convex, smooth Banach spaces with the property (K). As an application, the problem of finding a minimizer of a convex function is considered.