Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 400, Issue 2, Pages 597-614Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2012.11.059
Keywords
Bregman distance; Bregman strongly nonexpansive operator; Legendre function; Monotone mapping; Nonexpansive operator; Reflexive Banach space; Resolvent; Totally convex function
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Funding
- MEC [MTM2009-10696-C02-01]
- Junta de Andalucia [FQM-127]
- Israel Science Foundation [647/07]
- Graduate School of the Technion
- Fund for the Promotion of Research at the Technion
- Technion VPR Fund
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We present a detailed study of right and left Bregman strongly nonexpansive operators in reflexive Banach spaces. We analyze, in particular, compositions and convex combinations of such operators, and prove the convergence of the Picard iterative method for operators of these types. Finally, we use our results to approximate common zeros of maximal monotone mappings and solutions to convex feasibility problems. (C) 2012 Elsevier Inc. All rights reserved.
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