Bregman Distance and Strong Convergence of Proximal-Type Algorithms. (9th July 2013)

• Record Type: Journal Article
• Authors: Kuo, Li-Wei; Sahu, D. R.
• Other Names: Motreanu Dumitru Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-07-09
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/590519
• Languages: English
• ISSNs: 1085-3375

Abstract

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 Φ ( ∥ · ∥ ) . 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.