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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 590519, 12 pages
http://dx.doi.org/10.1155/2013/590519
Research Article

Bregman Distance and Strong Convergence of Proximal-Type Algorithms

1Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan
2Department of Mathematics, Banaras Hindu University, Varanasi 221005, India

Received 31 October 2012; Revised 7 March 2013; Accepted 7 March 2013

Academic Editor: Dumitru Motreanu

Copyright © 2013 Li-Wei Kuo and D. R. Sahu. 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.

Abstract

The purpose of this paper is to discuss some fundamental properties of Bregman distance, generalized projection operators, firmly nonexpansive mappings, and resolvent operators of set-valued monotone operators corresponding to a functional . We further study some proximal point algorithms for finding zeros of monotone operators and solving generalized mixed equilibrium problems in Banach spaces. Our results improve and extend some recent results concerning generalized projection operators corresponding to Bregman distance.