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Equilibrium problem using the method of set-valued analysis

Research Project

Project/Area Number 19740065
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionTokyo Institute of Technology

Principal Investigator

KIMURA Yasunori  Tokyo Institute of Technology, 大学院・情報理工学研究科, 助教 (20313447)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥2,690,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords均衡問題 / リゾルベント / Mosco収束 / 変分不等式問題 / 極大単調作用素 / 収縮射影法
Research Abstract

In this research, we deal with some nonlinear problems which have been applied to other research fields such as engineering, economics, and others. We investigated their relationship and algorithms for finding their solutions. We focused on the equilibrium problems and variational inequality problems and found their close relationship. We also proposed some approximation methods of the solutions to these problems by using the methods of set-valued analysis.

Report

(5 results)
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (56 results)

All 2010 2009 2008 2007 Other

All Journal Article (27 results) (of which Peer Reviewed: 22 results) Presentation (29 results)

  • [Journal Article] Some characterizations for a family of nonexpansive mappings and convergence of a generated sequence to their common fixed point2010

    • Author(s)
      Y.Kimura, K.Nakajo
    • Journal Title

      Fixed Point Theory and Applications Article ID 732872

      Pages: 16-16

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some characterizations for a family of nonexpansive mappings and convergence of a generated sequence to their common fixed point2010

    • Author(s)
      Y.Kimura, K.Nakajo
    • Journal Title

      Fixed Point Theory and Applications 2010

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shrinking projection methods and common zero point problems for a finite family of maximal monotone operators2010

    • Author(s)
      木村泰紀
    • Journal Title

      Proceedings of the Sixth International Conference on Nonlinear Analysis and Convex Analysis (to appear)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Further improvement of a coefficient condition for a weakly convergent iterative scheme2009

    • Author(s)
      Y.Kimura
    • Journal Title

      Nonlinear Analysis Series A: Theory, Methods & Applications 71

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a hybrid method for a family of relatively nonexpansive mappings in a Banach space2009

    • Author(s)
      Y.Kimura, W.Takahashi
    • Journal Title

      Journal of Mathematical Analysis and Applications 357

      Pages: 356-363

    • Related Report
      2009 Annual Research Report 2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Further improvement of a coefficient condition for a weakly convergent iterative scheme2009

    • Author(s)
      Y. Kimura
    • Journal Title

      Nonlinear Analysis Series A: Theory, Methods & Applications 71

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On a hybrid method for a family of relatively nonexpansive mappings in a Banach space2009

    • Author(s)
      Y. Kimura, W. Takahashi
    • Journal Title

      Journal of Mathematical Analysis and Applications 357

      Pages: 356-363

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Convexity of the set of fixed points of a quasi-pseudocontractive type Lipschitz mapping and the shrinking projection method2009

    • Author(s)
      Y.Kimura, K.Nakajo, W.Takahashi
    • Journal Title

      Scientiae Mathematicae Japonicae 70

      Pages: 213-220

    • NAID

      10025867833

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 一般化された近接点法と非線形写像の列について2009

    • Author(s)
      木村泰紀
    • Journal Title

      数理解析研究所講究録 1643

      Pages: 217-224

    • Related Report
      2009 Annual Research Report
  • [Journal Article] バナッハ空間での収縮射影法による不動点近似2009

    • Author(s)
      木村泰紀
    • Journal Title

      数理解析研究所講究録 1667

      Pages: 160-168

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Weak convergence of an iterative scheme with a weaker coefficient condition2009

    • Author(s)
      Y. Kimura
    • Journal Title

      Modeling, Computation and Optimization (In press)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strongly convergent iterative schemes for a sequence of nonlinear mappings2008

    • Author(s)
      Y.Kimura, K.Nakajo, W.Takahashi
    • Journal Title

      Journal of Nonlinear and Convex Analysis 9

      Pages: 407-416

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A generalized proximal point algorithm and implicit iterative schemes for a sequence of operators on Banach spaces2008

    • Author(s)
      Y.Kimura, W.Takahashi
    • Journal Title

      Set-Valued Analysis 16

      Pages: 597-619

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Maximal monotone operators and maximal monotone functions for equilibrium problems2008

    • Author(s)
      K.Aoyama, Y.Kimura, W.Takahashi
    • Journal Title

      Journal of Convex Analysis 15

      Pages: 395-409

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Maximal monotone operators and maximal monotone functions for equilibrium problems2008

    • Author(s)
      K. Aoyama, Y. Kimura, W. Takahashi
    • Journal Title

      Journal of Convex Analysis 15

      Pages: 395-409

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] バナッハ空間上の写像列に関する収束定理と係数条件2008

    • Author(s)
      木村泰紀
    • Journal Title

      数理解析研究所講究録 1615

      Pages: 165-124

    • Related Report
      2008 Annual Research Report
  • [Journal Article] An improvement of coefficient condition for weakly convergent iterative schemes2008

    • Author(s)
      Y. Kimura
    • Journal Title

      Proceedings of the Fifth International Conference on Nonlinear Analysis and Convex Analysis

      Pages: 85-93

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 均衡問題と解の近似について2008

    • Author(s)
      木村泰紀
    • Journal Title

      数理解析研究所講究録 1611

      Pages: 122-127

    • NAID

      110006852982

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Strongly convergent iterative schemes for a sequence of nonlinear mappings2008

    • Author(s)
      Y. Kimura, K. Nakajo, and W. Takahashi
    • Journal Title

      Journal of Nonlinear and Convex Analysis 9

      Pages: 407-416

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finding common fixed points of a countable family of nonexpansive mappings in a Banach space2007

    • Author(s)
      K. Aoyama, Y. Kimura, W. Takahashi, and M,Toyoda
    • Journal Title

      Scientiae Mathematicae Japonicae 66

      Pages: 89-99

    • NAID

      10019758613

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] バナッハ空間における均衡問題と関数の近似列について2007

    • Author(s)
      木村泰紀
    • Journal Title

      数理解析研究所講究録 1570

      Pages: 137-144

    • Related Report
      2007 Annual Research Report
  • [Journal Article] On a strongly nonexpansive sequence in Hilbert spaces2007

    • Author(s)
      K. Aoyama, Y. Kimura, W. Takahashi, and M,Toyoda
    • Journal Title

      Journal of Nonlinear and Convex Analysis 8

      Pages: 471-489

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong convergence theorems by a hybrid method for families of relatively nonexpansive mappings in Banach spaces

    • Author(s)
      Y. Kimura
    • Journal Title

      Proceedings of Asian Conference on Nonlinear Analysis and Optimization (In press)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Further improvement of a coefficient condition for a weakly convergent iterative scheme

    • Author(s)
      Y. Kimura
    • Journal Title

      Nonlinear Analysis Series A : Theory, Methods & Applications (In press)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A generalized proximal point algorithm and implicit iterative schemes for a sequence of operators on Banach spaces

    • Author(s)
      Y. Kimura and W. Takahashi
    • Journal Title

      Set-Valued Analysis

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maχimal monotone operators and maximal monotone functions for equilibrium problems

    • Author(s)
      K. Aoyama, Y. Kimura, and W. Takahashi
    • Journal Title

      Journal of Convex Analysis

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equilibrium problems and convergence of resolvents for a sequence of functions

    • Author(s)
      Y. Kimura
    • Journal Title

      Proceedings of the International Symposium on Banach and Function Spaces

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] 収縮射影法による不動点近似2010

    • Author(s)
      木村泰紀
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Shrinking projection methods for families of nonlinear mappings2009

    • Author(s)
      Y.Kimura
    • Organizer
      2009 Workshop on Nonlinear Analysis and Optimization
    • Place of Presentation
      National Taiwan Normal University, Taipei, Taiwan.
    • Year and Date
      2009-11-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Shrinking projection methods for families of nonlinear mappings2009

    • Author(s)
      Y. Kimura
    • Organizer
      2009 Workshop on Nonlinear Analysis and Optimization
    • Place of Presentation
      National Taiwan Normal University, Taipei, Taiwan
    • Year and Date
      2009-11-26
    • Related Report
      2009 Annual Research Report 2009 Self-evaluation Report
  • [Presentation] 収縮射影法に関する最近の成果2009

    • Author(s)
      木村泰紀
    • Organizer
      RIMS研究集会 非線形解析学と凸解析学の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-09-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] 単調作用素の零点問題と収縮射影法2009

    • Author(s)
      木村泰紀
    • Organizer
      RIMS研究集会 非加法性の数理と情報:凸解析との接点
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-08-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] バナッハ空間での収縮射影法による不動点近似2009

    • Author(s)
      木村泰紀
    • Organizer
      RIMS研究集会 バナッハ空間及び関数空間論における幾何学的構造の研究とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-05-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the shrinking projection methods for nonlinear mappings2009

    • Author(s)
      Y.Kimura
    • Organizer
      The Sixth International Conference on Nonlinear Analysis and Convex Analysis (NACA2009)
    • Place of Presentation
      Tokyo Institute of Technology, Tokyo, Japan
    • Year and Date
      2009-03-30
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] Coefficient conditions for a weakly convergent iterative scheme2009

    • Author(s)
      Y.Kimura
    • Organizer
      International Symposium on Nonlinear Analysis and Optimization 2009 (ISNAO2009)
    • Place of Presentation
      Pukyong National University, Busan, Korea.
    • Year and Date
      2009-02-10
    • Related Report
      2009 Final Research Report
  • [Presentation] Coefficient conditions for a weakly convergent iterative scheme2009

    • Author(s)
      Y. Kimura
    • Organizer
      International Symposium on Nonlinear Analysis and Optimization 2009 (ISNAO2009)
    • Place of Presentation
      Pukyong National University, Busan, Korea
    • Year and Date
      2009-02-10
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Coefficient conditions for a weakly convergent iterative scheme2009

    • Author(s)
      Y. Kimura
    • Organizer
      International Symposium on Nonlinear Analysis and Optimization 2009 (ISNA02009)
    • Place of Presentation
      Pukyong National University, Busan, Korea.
    • Year and Date
      2009-02-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] A generalization of the proximal point algorithm and a countable family of nonlinear mappings2008

    • Author(s)
      Y.Kimura
    • Organizer
      Asian Conference on Nonlinear Analysis and Optimization (NAO-Asia2008)
    • Place of Presentation
      Kunibiki Messe, Matsue, Japan.
    • Year and Date
      2008-09-16
    • Related Report
      2009 Final Research Report
  • [Presentation] A generalization of the proximal point algorithm and a countablefamily of nonlinear mappings2008

    • Author(s)
      Y. Kimura
    • Organizer
      Asian Conference on Nonlinear Analysis and Optimization(NAO-Asia2008)
    • Place of Presentation
      Kunibiki Messe, Matsue, Japan
    • Year and Date
      2008-09-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] On generalized proximal point algorithms and sequence of nonlinear mappings2008

    • Author(s)
      木村泰紀
    • Organizer
      RIMS研究集会非線形解析学と凸解析学の研究
    • Place of Presentation
      京都大学
    • Year and Date
      2008-09-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] Convergence of an iterative scheme generated by a sequence of nonlinear operators2008

    • Author(s)
      Y.Kimura
    • Organizer
      World Congress of Nonlinear Analysts (WCNA2008)
    • Place of Presentation
      Hyatt Grand Cypress Resort, Orlando, FL, USA.
    • Year and Date
      2008-07-02
    • Related Report
      2009 Final Research Report
  • [Presentation] Convergence of an iterative scheme generated by a sequence of nonlinear operators2008

    • Author(s)
      Y. Kimura
    • Organizer
      World Congress of Nonlinear Analysts (WCNA2008)
    • Place of Presentation
      Hyatt Grand Cypress Resort, Orlando, FL, USA
    • Year and Date
      2008-07-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] Iterative methods for approximation of a solution to nonlinear operator inclusions2008

    • Author(s)
      Y.Kimura
    • Organizer
      ICNPAA2008 Mathematical Problems in Engineering, Aerospace and Sciences
    • Place of Presentation
      University of Genoa, Genoa, Italy.
    • Year and Date
      2008-06-27
    • Related Report
      2009 Final Research Report
  • [Presentation] Iterative methods for approximation of a solution to nonlinear operator inclusions2008

    • Author(s)
      Y. Kimura
    • Organizer
      ICNPAA2008 Mathematical Problems in Engineering, Aerospace and Sciences
    • Place of Presentation
      University of Genoa, Genoa, Italy
    • Year and Date
      2008-06-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] Convergence theorems and coefficient conditions for a sequence of mappings in Banach space2008

    • Author(s)
      木村泰紀
    • Organizer
      RIMS研究集会バナッハ空間及び関数空間論の最近の進展どその応用
    • Place of Presentation
      京都大学
    • Year and Date
      2008-06-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] Weak convergence of an iterative scheme with a weaker coefficient condition2008

    • Author(s)
      Y.Kimura
    • Organizer
      International Conference on Modeling, Computation and Optimization (ICMCO-08)
    • Place of Presentation
      Indian Statistical Institute, Delhi, India.
    • Year and Date
      2008-01-10
    • Related Report
      2009 Final Research Report
  • [Presentation] Weak convergence of an iterative scheme with a weaker coefficient condition2008

    • Author(s)
      Y. Kimura
    • Organizer
      International Conference on Modeling, Computation and Optimization (ICMCO-08)
    • Place of Presentation
      Indian Statistical Institute, Delhi, India
    • Year and Date
      2008-01-10
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Weak convergence of an iterative scheme with a weaker coefficient condition2008

    • Author(s)
      Y.
    • Organizer
      International Conference on Modeling,
    • Place of Presentation
      Indian Statistical Institute, Delhi, India.
    • Year and Date
      2008-01-10
    • Related Report
      2007 Annual Research Report
  • [Presentation] Iterative schemes with a sequence of resolvents and set-convergence2007

    • Author(s)
      Y.
    • Organizer
      International Symposium on Nonlinear Analysis and Convex Analysis 2007 (ISCACA2007)
    • Place of Presentation
      National Sun Yat-sen University, Kaohsiung, Taiwan
    • Year and Date
      2007-11-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] A sequence of resolvents and set-convergence2007

    • Author(s)
      Y.Kimura
    • Organizer
      Japan-Thailand Joint Seminar on Fixed Point Algorithms in Optimization
    • Place of Presentation
      Tokyo Institute of Technology, Tokyo, Japan.
    • Year and Date
      2007-09-07
    • Related Report
      2009 Final Research Report
  • [Presentation] A sequence of resolvents and set-convergence2007

    • Author(s)
      Y.
    • Organizer
      Japan-Thailand Joint Seminar on Fixed Point Algorit hms in Optimization
    • Place of Presentation
      Tokyo Institute of Technology, Tokyo, Japan
    • Year and Date
      2007-09-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] An equilibrium problems and approximation of its solutions2007

    • Author(s)
      Y.
    • Organizer
      RIMS Symposium: Nonlinear analysis and convex ana lysis
    • Place of Presentation
      Kyoto University, Kyoto, Japan
    • Year and Date
      2007-09-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] Monotone operators and equilibrium problems in Banach spaces2007

    • Author(s)
      Y.Kimura
    • Organizer
      The 8th International Conference on Fixed Point Theory and Its Applications (ICFPTA2007)
    • Place of Presentation
      Chiang Mai University, Chiang Mai, Thailand.
    • Year and Date
      2007-07-16
    • Related Report
      2009 Final Research Report
  • [Presentation] Monotone operators and equilibrium problems in Banach spaces2007

    • Author(s)
      Y.
    • Organizer
      The 8th International Conference on Fixed Point Theory and Its Applications (ICFPTA2007)
    • Place of Presentation
      Chiang Mai University, Chiang Mai, Thailand
    • Year and Date
      2007-07-16
    • Related Report
      2007 Annual Research Report
  • [Presentation] Equilibrium problems on Banach spaces and maximal monotonicity2007

    • Author(s)
      Y.
    • Organizer
      RIMS Symposium:Banach spaces,
    • Place of Presentation
      Kyoto University, Kyoto, Japan
    • Year and Date
      2007-06-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] Equilibrium problems and maximal monotonicity2007

    • Author(s)
      Y.
    • Organizer
      The Fifth International Conference on Nonlinear Analysis and Convex Analysis (NACA2007)
    • Place of Presentation
      National Tsing-Hua University, Hsihchu, Taiwan.
    • Year and Date
      2007-06-01
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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