Abstract and Applied Analysis
Volume 2006 (2006), Article ID 84919, 39 pages

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

Dan Butnariu1 and Elena Resmerita2

1Department of Mathematics, University of Haifa, Haifa 31905, Israel
2Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, Linz 4040, Austria

Received 25 July 2004; Accepted 6 April 2005

Copyright © 2006 Dan Butnariu and Elena Resmerita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations.