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

Dan Butnariu | Zendy; Elena Resmerita | Zendy

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

Author(s) -

Dan Butnariu,

Elena Resmerita

Publication year - 2006

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/aaa/2006/84919

Subject(s) - mathematics , bregman divergence , convexity , banach space , operator (biology) , regular polygon , convergence (economics) , consistency (knowledge bases) , iterative method , convex function , type (biology) , mathematical optimization , mathematical analysis , discrete mathematics , geometry , biochemistry , chemistry , ecology , repressor , biology , transcription factor , financial economics , economics , gene , economic growth

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

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