@article{594049d201c6484da6fd6c8e07f62210,
title = "Bregman strongly nonexpansive operators in reflexive Banach spaces",
abstract = "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.",
keywords = "Bregman distance, Bregman strongly nonexpansive operator, Legendre function, Monotone mapping, Nonexpansive operator, Reflexive Banach space, Resolvent, Totally convex function",
author = "Victoria Mart{\'i}n-M{\'a}rquez and Simeon Reich and Shoham Sabach",
note = "Funding Information: The first author was partially supported by MEC (Grant MTM2009-10696-C02-01 ) and by the Junta de Andaluc{\'i}a (Grant FQM-127 ); the second and third authors were partially supported by the Israel Science Foundation (Grant 647/07 ), the Graduate School of the Technion , the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund . Part of the research pertaining to this paper was carried out when the authors were visiting each other{\textquoteright}s institutions. They thank their colleagues for their kind hospitality. The authors are also grateful to an anonymous referee for a thorough and detailed report with many helpful comments and suggestions.",
year = "2013",
month = apr,
day = "15",
doi = "https://doi.org/10.1016/j.jmaa.2012.11.059",
language = "الإنجليزيّة",
volume = "400",
pages = "597--614",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",
}