Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces

Toru Maruyama, Wataru Takahashi, Masayuki Yao

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

In this paper, we first consider a broad class of nonlinear mappings containing the class of generalized hybrid mappings defined by Kocourek, Takahashi and Yao [11] in a Hilbert space. Then, we prove a fixed point theorem, a mean ergodic theorem of Baillon's type [2] and a weak convergence theorem of Mann's type [14] for these nonlinear mappings in a Hilbert space.

Original languageEnglish
Pages (from-to)185-197
Number of pages13
JournalJournal of Nonlinear and Convex Analysis
Volume12
Issue number1
Publication statusPublished - 2011 Apr 1

Keywords

  • Fixed point
  • Hilbert space
  • Hybrid mapping
  • Mean convergence
  • Nonexpansive mapping
  • Nonspreading mapping

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics

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