Iterations of paracontractions and firmaly nonexpansive operators with applications to feasibility and optimization

Abstract

A generalized “measure of distance” defined by . is generated from any member f of the class of Bregman functions. Although it is not. technically speaking. a distance function. it has been used in the past to define and study projection operators. In this paper we give new definitions of paracont ractions. convex combinations. and firmly nonexpansivc operators. based on D_f (x,y), and study sequential and simultaneous iterative algorithms employing them for the solution of the problem of finding a common asymptotic fixed point of a family of operators. Applications to the convex feasibility problem. to optimization and to monotone operator theory are also included.