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Nonlinear problems related to fixed point theory

Research Project

Project/Area Number 25400141
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKyushu Institute of Technology

Principal Investigator

Suzuki Tomonari  九州工業大学, 大学院工学研究院, 教授 (00303173)

Co-Investigator(Kenkyū-buntansha) 加藤 幹雄  信州大学, 工学部, 非常勤講師 (50090551)
本田 あおい  九州工業大学, 大学院情報工学研究院, 准教授 (50271119)
仙葉 隆  九州工業大学, 大学院工学研究院, 教授 (30196985)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords不動点 / best proximity point / nonspreading mapping / Chatterjea mapping / ν-generalized metric / absolute norm / p-uniform convexity / q-uniform smoothness / contraction / generalized nonexpansive / Kadec-Klee property / weak P-property
Outline of Final Research Achievements

In these three years, we have several results in nonlinear problems related to fixed point theory. For example, we have introduced new classes of nonlinear mappings (Chatterjea mapping, Condition (CC)) and studied basic properties, existence of fixed points and convergence theorems. We have given examples of nu-generalized metric spaces that do not have the compatible topology. Also we have proved that every 3-generalized metric space has the compatible topology. We have obtained a new sufficient and necessary condition for successive approximation.

Report

(4 results)
  • 2016 Final Research Report ( PDF )
  • 2015 Annual Research Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (22 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (1 results) Journal Article (16 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 15 results,  Open Access: 10 results,  Acknowledgement Compliant: 9 results) Presentation (5 results) (of which Int'l Joint Research: 1 results,  Invited: 2 results)

  • [Int'l Joint Research] King Abdulaziz University(Saudi Arabia)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivitiy2016

    • Author(s)
      K. Fujie and T. Senba
    • Journal Title

      Discrete and Continuous Dynamical Systems - Series B

      Volume: 21 Issue: 1 Pages: 81-102

    • DOI

      10.3934/dcdsb.2016.21.81

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Caristi's fixed point theorem and Subrahmanyam's fixed point theorem in nu-generalized metric spaces2015

    • Author(s)
      Badriah Alamri, Tomonari Suzuki, Liaqat Ali Khan
    • Journal Title

      Journal of Function Spaces

      Volume: 2015 Pages: 709391-709391

    • DOI

      10.1155/2015/709391

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point \uppercase\expandafter{\romannumeral2}2015

    • Author(s)
      Tomonari Suzuki, Badriah Alamri
    • Journal Title

      Fixed Point Theory and Applications

      Volume: 2015 Issue: 1

    • DOI

      10.1186/s13663-015-0302-9

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Fixed point theorems for new nonlinear mappings satisfying Condition (CC)2015

    • Author(s)
      Misako Kikkawa, Tomonari Suzuki
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 1 Pages: 37-52

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Only 3-generalized metric spaces have a compatible symmetric topology2015

    • Author(s)
      Tomonari Suzuki, Badriah Alamri, Misako Kikkawa
    • Journal Title

      Open Mathematics

      Volume: 13 Issue: 1 Pages: 510-517

    • DOI

      10.1515/math-2015-0048

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Edelstein's fixed point theorem in generalized metric spaces2015

    • Author(s)
      Tomonari Suzuki, Badriah Alamri, Misako Kikkawa
    • Journal Title

      Journal of Nonlinear and Convex Analysis

      Volume: 16 Pages: 2301-2309

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the uniform non-l1n-ness and new classes of convex functions2015

    • Author(s)
      Mikio Kato, Takayuki Tamura
    • Journal Title

      Journal of Nonlinear and Convex Analysis

      Volume: 16 Pages: 2279-2295

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fixed point theorems for a new nonlinear mapping similar to a nonspreading mapping2014

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Fixed Point Theory and Applications

      Volume: 2014 Issue: 1

    • DOI

      10.1186/1687-1812-2014-47

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Generalized metric spaces do not have the compatible topology2014

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Abstract and Applied Analysis

      Volume: 2014 Pages: 458098-458098

    • DOI

      10.1155/2014/458098

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] p-uniform convexity and q-uniform smoothness of absolute normalized norms on C22014

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Abstract and Applied Analysis

      Volume: 2014 Pages: 746309-746309

    • DOI

      10.1155/2014/746309

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On a new geometric constant related to the modulus of smoothness of a Banach space2014

    • Author(s)
      Yasuji Takahashi, Mikio Kato
    • Journal Title

      Acta Math. Sinica English Ser.

      Volume: 30 Issue: 9 Pages: 1526-1538

    • DOI

      10.1007/s10114-014-2782-7

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A fairness relation based on the asymmetric Choquet integral and its application in network2014

    • Author(s)
      Aoi Honda, Mario Koeppen
    • Journal Title

      Journal of Applied Mathematics

      Volume: 2014 Pages: 725974-725974

    • DOI

      10.1155/2014/725974

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On a weak attractor of a class of PDEs with degenerate diffusion and chemotaxis2014

    • Author(s)
      Messoud Efendiev, Takasi Senba, Anna Zhigun
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 66 Issue: 4 Pages: 1133-1153

    • DOI

      10.2969/jmsj/06641133

    • NAID

      130004705997

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] An elementary proof of the 2-dimensional version of the Brouwer fixed point theorem2014

    • Author(s)
      Yukio Takeuchi; Tomonari Suzuki
    • Journal Title

      Bulletin of the Kyushu Institute of Technology

      Volume: 61 Pages: 1-6

    • NAID

      120005441896

    • Related Report
      2013 Research-status Report
  • [Journal Article] A Reich-type convergence theorem for generalized nonexpansive mappings in uniformly convex Banach spaces2013

    • Author(s)
      Safeer Hussain Khan; Tomonari Suzuki
    • Journal Title

      Nonlinear Analysis, Theory, Methods & Applications

      Volume: 80 Pages: 211-215

    • DOI

      10.1016/j.na.2012.09.005

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The existence of best proximity points with the weak P-property2013

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Fixed Point Theory and Applications

      Volume: 2013 Issue: 1

    • DOI

      10.1186/1687-1812-2013-259

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] nu-generalized metric space の位相2016

    • Author(s)
      Tomonari Suzuki
    • Organizer
      日本数学会年会
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-18
    • Related Report
      2015 Annual Research Report
  • [Presentation] Topology on nu-generalized metric spaces2015

    • Author(s)
      Tomonari Suzuki
    • Organizer
      The Fifth International Symposium on Banach and Function Spaces 2015
    • Place of Presentation
      九州工業大学
    • Year and Date
      2015-09-03
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Condition {\rm (CC)} に関する不動点定理2015

    • Author(s)
      T. Suzuki
    • Organizer
      関数解析学の研究とその応用
    • Place of Presentation
      新潟大学
    • Year and Date
      2015-01-30
    • Related Report
      2014 Research-status Report
  • [Presentation] The Brouwer fixed point theorem2013

    • Author(s)
      Yukio Takeuchi; Tomonari Suzuki
    • Organizer
      Twenty second International Conference of FIM (Forum for Interdisciplinary Mathematics) on Interdisciplinary Mathematics, Statistics and Computational Techniques
    • Place of Presentation
      北九州国際会議場
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Fixed point theorems for Chatterjea mappings2013

    • Author(s)
      Tomonari Suzuki
    • Organizer
      International Conference on Nonlinear Analysis and Optimization
    • Place of Presentation
      National Sun Yat-sen University, Taiwan
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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