ITERATIVE METHODS FOR APPROXIMATION OF FIXED POINTS AND THEIR APPLICATIONS

• Takahashi Wataru

  Tokyo Institute of Technology

抄録

In this article, we deal with iterative methods for approximation of fixed points and their applications, We first discuss fixed point theorems for a nonexpansive mapping or a family of nonexpansive mappings. In particular, we state a fixed point theorem which answered affirmatively a problem posed during the Conference on Fixed Point Theory and Applications held at CIRM, Marseille-Luminy, 1989. Then we discuss nonlinear ergodic theorems of Baillon's type for nonlinear semigroups of nonexpansive mappings. In particular, we state nonlinear ergodic theorems which answered affirmatively the problem posed during the Second World Congress on Nonlinear Analysts, Athens, Greece, 1996. Next, we deal with weak and strong convergence theorems of Mann's type and Halpern's type in a Banach space. Finally, using these results, we consider the feasibility problem by convex combinations of nonexpansive retractions and the convex minimization problem of finding a minimizer of a convex function.

収録刊行物

• 日本オペレーションズ・リサーチ学会論文誌

  日本オペレーションズ・リサーチ学会論文誌 43 (1), 87-108, 2000

  公益社団法人 日本オペレーションズ・リサーチ学会

キーワード

• Management Science and Operations Research
• General Decision Sciences

詳細情報

• CRID: 1390282679086140544
• NII論文ID: 110001183904
• NII書誌ID: AA00703935
• DOI: 10.15807/jorsj.43.87
• ISSN: 21888299
• ISSN: 04534514
• NDL書誌ID: 5316473
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I5316473
• Web Site: https://www.jstage.jst.go.jp/article/jorsj/43/1/43_KJ00001201961/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可