Bregman strongly nonexpansive operators in reflexive Banach spaces

Victoria Martín-Márquez, Simeon Reich, Shoham Sabach

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)597-614
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume400
Issue number2
DOIs
StatePublished - 15 Apr 2013

Keywords

  • Bregman distance
  • Bregman strongly nonexpansive operator
  • Legendre function
  • Monotone mapping
  • Nonexpansive operator
  • Reflexive Banach space
  • Resolvent
  • Totally convex function

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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