Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces

Abstract

The aim of this paper is twofold. First, several basicmathematical concepts involved in the construction and study ofBregman type iterative algorithms are presented from a unifiedanalytic perspective. Also, some gaps in the current knowledgeabout those concepts are filled in. Second, we employ existingresults on total convexity, sequential consistency, uniformconvexity and relative projections in order to define and studythe convergence of a new Bregman type iterative method of solvingoperator equations. Copyright © 2006 D. Butnariu and E. Resmerita.