Nonlinear Functional Analysis and Nonlinear Problem by Fixed Point Theory

• Project/Area Number: 18740078
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: University of Yamanashi (2008); Shibaura Institute of Technology (2006-2007)
• Principal Investigator: ATSUSHIBA Sachiko University of Yamanashi, 教育人間科学部, 准教授 (20327761)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,810,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000); Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
• Keywords: 不動点 / 非拡大写像 / 擬非拡大写像 / 非線形最適化問題 / 弱収束 / 強収束擬射影 / 制約可能性問題 / 強収束 / 擬射影 / 非拡大半群 / Banach空間 / Opial条件

Research Abstract

本研究では、不動点定理・不動点理論に関する非線形関数解析学の基礎理論を体系的に構成し、それをもとに、不動点近似に関する多くの成果を得られた。つまり、非線形問題へ結びつく、不動点への弱収束定理および強収束定理や不動点の存在に関する多くの研究成果を得られた。さらにその得られた不動点理論・不動点近似の成果の立場から非線形最適化問題、制約可能性問題、経済均衡問題等の非線形問題を再構成して、不動点近似に帰着させる形で非線形問題の解への収束定理に関する成果まで得られた。

Research Products

• [Journal Article] The Sequences by the Hybrid Type Method and the Existence of Common Fixed Points of Nonexpansive Semigroups in a Hilbert Space (2009)
  • Author(s): Sachiko Atsushiba and Wataru Takahashi
  • Journal Title: Nonlinear Analysis and Optimization (印刷中)
  • Peer Reviewed
• [Journal Article] On the Sequences by the Hybrid Type Method and the Existence of Common Fixed Points of Families of Nonexpansive Mappings (2009)
  • Author(s): Sachiko Atsushiba
  • Journal Title: 非線形解析学と凸解析学の研究(Nonlinear analysis and convex analysis) (印刷中)
• [Journal Article] Approximating Common Fixed Points of Nonexpansive Semigroups in Banach Spaces by Metric Projections (2008)
  • Author(s): Sachiko Atsushiba and Wataru Takahashi
  • Journal Title: Scientiae Mathematicae Japonicae Vol.632 Pages: 323-331
  • NAID: 10025094512
  • Peer Reviewed
• [Journal Article] Strong Convergence Theorem for a Family of Relatively Nonexpansive Mappings in Banach Spaces (2008)
  • Author(s): Sachiko Atsushiba
  • Journal Title: Fixed Point Theory and its Applications Vol.8 Pages: 19-28
  • Peer Reviewed
• [Journal Article] Approximating Common Fixed Points of Nonexpansive Semigroups in Banach Spaces by Metric Projections (2008)
  • Author(s): Sachiko Atsushiba and Wataru Takahashi
  • Journal Title: Scientiae Mathematicae Japonicae 63 Pages: 323-331
  • NAID: 10025094512
  • Peer Reviewed
• [Journal Article] Weak Convergence Theorem for a Family of Relatively Nonexpansive Mappings in Banach Spaces (2008)
  • Author(s): Sachiko Atsushiba and Wataru Takahashi
  • Journal Title: Nonlinear Analysis and Convex Analysis 5 Pages: 47-59
  • Peer Reviewed
• [Journal Article] Strong Convergence Theorem for a Family of Relatively Nonexpansive Mappings in Banach Spaces (2008)
  • Author(s): Sachiko Atsushiba
  • Journal Title: Fixed Point Theory and its Applications 8 Pages: 19-28
  • Peer Reviewed
• [Journal Article] Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Banach Spaces by Browder's Type Iterations (2008)
  • Author(s): Sachiko Atsushiba
  • Journal Title: Banach and Functional Spaces 2 Pages: 293-308
  • Peer Reviewed
• [Journal Article] 距離射影を用いた非拡大写像族の共通不動点近似について (2008)
  • Author(s): 厚芝幸子
  • Journal Title: バナッハ空間及び関数空間論の最近の進展とその応用(Recent results of Banach and function spaces and its applications) 1615 Pages: 34-43
• [Journal Article] Weak and strong convergence theorems for a family of relatively nonexpansive mappings in Banach spaces (2008)
  • Author(s): Sachiko Atsushiba
  • Journal Title: 非線形解析学と凸解析学の研究(Nonlinear analysis and convex analysis), RIMS Kokyuroku 1611 Pages: 67-75
• [Journal Article] Weak Convergence Theorems for a Family of Relatively Nonexpansive Mappings in Banach Spaces (2008)
  • Author(s): Sachiko, Atsushiba・Wataru, Takahashi
  • Journal Title: Nonlinear Analysis and Convex Analysis (印刷中)
  • Peer Reviewed
• [Journal Article] Strong Convergence Theorems for a Family of Relatively Nonexpansive Mappings in Banach Spaces (2008)
  • Author(s): Sachiko, Atsushiba
  • Journal Title: Fixed Point Theory (印刷中)
  • Peer Reviewed
• [Journal Article] Convergence of Iterative Sequences for Nonlinear Operators in Banach Spaces (2008)
  • Author(s): Sachiko, Atsushiba
  • Journal Title: 第16回関数空間セミナー報告集, 北海道テクニカルレポート 128 Pages: 68-73
• [Journal Article] 擬非拡大写像族に対する弱収束定理について (2008)
  • Author(s): Sachiko, Atsushiba
  • Journal Title: 非加法の数理と情報:非線形性・非可換性との接点京都大学数理解析研究所講究録 (印刷中)
• [Journal Article] Convergence of Iterative Sequences for Nonlinear Operators in Banach Spaces (2008)
  • Author(s): Sachiko, Atsushiba
  • Journal Title: Nonlinear analysis and convex analysis, RIMS Kokyuroku (印刷中)
• [Journal Article] Approximating Zero Points of Accretive Operators by Implicit Iterative Sequences (2007)
  • Author(s): Sachiko Atsushiba
  • Journal Title: Taiwanese Journal of Mathematics Vol.11 Pages: 807-818
  • Peer Reviewed
• [Journal Article] Approximating Zero Points of Accretive Operators by Implicit Iterative Sequences (2007)
  • Author(s): Sachiko, Atsushiba
  • Journal Title: Taiwannese Journal of Mathematics 11 Pages: 807-818
  • Peer Reviewed
• [Journal Article] Weak Convergence Theorems for a Countable Family of Nonexpansive Mappings in Banach Spaces which satisfy Opial's condition (2007)
  • Author(s): Sachiko, Atsushiba
  • Journal Title: Applied Functional Analysis,-Information Science and Related Topics- 1 Pages: 153-168
  • Peer Reviewed
• [Journal Article] Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in General Banach Spaces (2007)
  • Author(s): Sachiko Atsushiba
  • Journal Title: Nonlinear Analysis and Convex Anlysis 4 Pages: 47-60
• [Journal Article] Weak and Strong Convergence of Mann type and Implicit Iterations for Nonexpansive Semigroups in Banach Spaces (2007)
  • Author(s): Sachiko Atsushiba, Wataru Takahashi
  • Journal Title: Scientiae Mathematicae Japonicae 65 Pages: 147-160
• [Journal Article] Strong and Weak Convergence Theorems for a Countable Family of Nonexpansive Mappings in Banach Spaces (2006)
  • Author(s): Sachiko Atsushiba
  • Journal Title: バナッハ空間及び関数空間の構造の研究,RIMS Kokyuroku 1520 Pages: 45-52
• [Journal Article] Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Banach Spaces by Browder's type iterations
  • Author(s): Sachiko Atsushiba
  • Journal Title: Banach and Functional Spaces (印刷中)
• [Journal Article] Weak Convergence Theorems for a Countable Family of Nonexpansive Mappings in Banach Spaces which satisfy Opial's condition
  • Author(s): Sachiko Atsushiba
  • Journal Title: Applied Functional Analysis,-Information Science and Related Topics- (印刷中)
• [Journal Article] Weak and Strong Convergence of Implicit Iterative Sequences for Nonlinear Operators
  • Author(s): Sachiko Atsushiba
  • Journal Title: 非線形解析学と凸解析学研究、RIMS Kokyurok (印刷中)
• [Presentation] On the sequences by the hybrid method and convergence theorems for nonexpansive mappings (2009)
  • Author(s): Sachiko Atsushiba
  • Organizer: The Sixth International Conference on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: Tokyo Institute of Technology, Tokyo, Japan
  • Year and Date: 2009-03-29
• [Presentation] On the Sequences by the Hybrid Type Method and Convergence Theorems for Nonlinear Mappings (2009)
  • Author(s): Sachiko Atsushiba
  • Organizer: The International Symposium on Nonlinear Analysis and Optimization 2009
  • Place of Presentation: Pukyong National University, Korea
  • Year and Date: 2009-02-10
• [Presentation] Strong convergence theorems for nonlinear mapping in Banach spaces (2008)
  • Author(s): Sachiko Atsushiba
  • Organizer: The Asian Conference on Nonlinear Analysis and Optimization
  • Place of Presentation: Kunibiki Messe, Matsue, Japan
  • Year and Date: 2008-09-23
• [Presentation] Approximation of Common Fixed Points of Nonlinear Mappings by Projections (2008)
  • Author(s): Sachiko Atsushiba
  • Organizer: 非線形解析学と凸解析学の研究(Nonlinear Analysisand Convex Analysis)
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-09-02
• [Presentation] Approximating Common Fixed Points of Families of Nonexpansive Mappings in Banach Spaces by Metric Projections (2008)
  • Author(s): Sachiko Atsushiba
  • Organizer: The 9th International Symposium on Generalized Convexity and Generalized Monotonicity 2008
  • Place of Presentation: College of Science, National Sun Yat-sen University, Kaohsiung, Taiwan
  • Year and Date: 2008-07-21
• [Presentation] Approximating common fixed points of families of nonexpansive mappings in Banach spaces by metric projections (2008)
  • Author(s): Sachiko Atsushiba
  • Organizer: The 9th International Symposium on Generalize Convexity and Generalized Monotonicity 2008
  • Place of Presentation: College of Science, National Sun Yat-sen University, Kaohsiung, Taiwan
  • Year and Date: 2008-07-21
• [Presentation] Approximating Common Fixed Points of Nonexpansive Semigroups in Banach Spaces by Metric Projections (2008)
  • Author(s): Sachiko Atsushiba
  • Organizer: バナッハ空間及び関数空間論の最近の進展とその応用
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-06-04
• [Presentation] Banach空間における非線形写像族の共通不動点への収束定理 (2008)
  • Author(s): 厚芝幸子
  • Organizer: 2008年度 日本数学会年会 実函数論分科会
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-25
• [Presentation] Convergence of Iterative Sequences for Nonlinear Operators in Banach Spaces (2007)
  • Author(s): 厚芝幸子
  • Organizer: 第16回関数空間セミナー
  • Place of Presentation: 東京理科大学
  • Year and Date: 2007-12-25
• [Presentation] Strong Convergence Theorems for a Countable Family of Noneexpansive Mappings (2007)
  • Author(s): Sachiko, Atsushiba
  • Organizer: Japan-Thailand Joint Seminar on Fixed Point Algorithms in Optmization
  • Place of Presentation: 東京工業大学
  • Year and Date: 2007-09-07
• [Presentation] Convergence Theorems for Relatively Nonexpansive Mappings (2007)
  • Author(s): Sachiko, Atsushiba
  • Organizer: 2007 RIMS Workshop on Nonlinear Analysis and Convex Analysis
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-09-03
• [Presentation] Convergence of approximated sequences for nonlinear operators in Banach spaces (2007)
  • Author(s): Sachiko, Atsushiba
  • Organizer: 非加法の数理と情報:非線形性・非可換性との接点
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-08-14
• [Presentation] Convergence Theorems for Relatively Nonexpansive Mappings in Banach Spaces (2007)
  • Author(s): Sachiko, Atsushiba
  • Organizer: The 8th International Conference on Fixed Point Theory and Applications 2007
  • Place of Presentation: Chiang Mai Univesity, Chiang Mai, Thailand
  • Year and Date: 2007-07-16
• [Presentation] Viscosity approximation methods for Families of Nonexpansive Mappings in Banach Spaces (2007)
  • Author(s): Sachiko, Atsushiba
  • Organizer: The Fifth International Conference on Nonlinear Analysis and Convex Analysis (NACA2007)
  • Place of Presentation: Natinal Tsing Hua Univ., Hsinchu, Taiwan
  • Year and Date: 2007-06-01