TY - JOUR
T1 - Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces
AU - Butnariu, Dan
AU - Resmerita, Elena
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=31844434904&partnerID=8YFLogxK
U2 - 10.1155/AAA/2006/84919
DO - 10.1155/AAA/2006/84919
M3 - Article
AN - SCOPUS:31844434904
SN - 1085-3375
VL - 2006
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
M1 - 84919
ER -