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Fixed Point Theory and Topological and Geometry Structure

Research Project

Project/Area Number 16K05207
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)
Project Period (FY) 2016-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords不動点 / contraction / ν-generalized metric / τ-distance / semimetric space / semicompleteness / 完備距離空間 / 距離完備性 / 縮小写像 / compatible な位相 / 縮小写像の条件 / Condition (B) / 解析学
Outline of Final Research Achievements

We studied fixed point theory in metric spaces. For example, we proved a new generalization of both Bogin's fixed point theorem and Ciric's fixed point theorem in complete metric spaces. In the proof, we gave a new method. Also, we introduced the concept of τ'-distance which is a very slight generalization of τ-distance and which is more natural than τ-distance. Using this concept, we proved some related theorems. In metric fixed point theory, there are several contractive conditions. We discussed these conditions by a unified method.
We studied several spaces which do not have rich structure. For example, we prove that a ν-generalized metric space has both strongly compatible topology and the strongest sequentially compatible topology. Also, we proved Caristi's fixed point theorem in (Σ,≠)-complete semimetric spaces.

Academic Significance and Societal Importance of the Research Achievements

完備距離空間における不動点理論は1960年代と1970年代に大きく発展した。その後、本質的に新しい不動点定理は証明されなかったように思える。今回得られた不動点定理は証明の手法もとても新しく、今後の発展が期待できる。τ'-distance の導入や縮小条件に関する結果は、今後の議論展開を容易にするため、新たな発展へ寄与できると思われる。
最近、 semimetric space や ν-generalized metric space といった弱い構造しか持たない空間での研究が盛んに行われている。本研究もその一部であり、得られた成果を用いて、さらに精密な研究が行われると期待できる。

Report

(9 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (48 results)

All 2023 2020 2019 2018 2017 2016

All Journal Article (37 results) (of which Peer Reviewed: 32 results,  Open Access: 20 results,  Acknowledgement Compliant: 5 results) Presentation (11 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results)

  • [Journal Article] Some comments on τ-distance and existence theorems in complete metric spaces2023

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Filomat

      Volume: 37 Issue: 23 Pages: 7981-7992

    • DOI

      10.2298/fil2323981s

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 距離もどきの関数τ-DISTANCEについて2023

    • Author(s)
      鈴木智成
    • Journal Title

      日本大学経済学部研究紀要

      Volume: 98 Pages: 259-268

    • Related Report
      2023 Annual Research Report
  • [Journal Article] Some comments on τ-distance and existence theorems in complete metric spaces2023

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      FILOMAT

      Volume: 23

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Several completenesses on ν-generalized metric spaces2020

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Bulletin of the Kyushu Institute of Technology

      Volume: 67 Pages: 29-42

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] Some metrization problem on \nu-generalized metric spaces2019

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas

      Volume: 113 Issue: 2 Pages: 1267-1278

    • DOI

      10.1007/s13398-018-0544-6

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Jachymski-Matkowski-Swiatkowski's fixed point theorem2019

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Applicable Analysis and Discrete Mathematics

      Volume: 13 Issue: 2 Pages: 632-642

    • DOI

      10.2298/aadm170430024s

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Comments on some existence theorems of best proximity points for contractive-type mappings2019

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

      Bulletin of the Kyushu Institute of Technology

      Volume: 66 Pages: 1-14

    • NAID

      120006596468

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] The strongly compatible topology on nu-generalized metric spaces2018

    • Author(s)
      Suzuki Tomonari
    • Journal Title

      Revista de la Real Academia de Ciencias Exactas, F?sicas y Naturales. Serie A. Matem?ticas

      Volume: 112 Issue: 1 Pages: 301-309

    • DOI

      10.1007/s13398-017-0380-0

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Fixed point theorems for contractions of rational type in complete metric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Nonlinear Science and its Applications. JNSA

      Volume: 11 Issue: 01 Pages: 98-107

    • DOI

      10.22436/jnsa.011.01.08

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A generalization of Hegedus-Szilagyi's fixed point theorem in complete metric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Fixed Point Theory and Applications

      Volume: 2018 Issue: 1 Pages: 2018-2018

    • DOI

      10.1186/s13663-017-0625-9

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Caristi's fixed point theorem in semimetric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Fixed Point Theory and Applications

      Volume: 20 Issue: 1

    • DOI

      10.1007/s11784-018-0492-y

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Fixed point theorems for single- and set-valued F-contractions in b-metric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Fixed Point Theory and Applications

      Volume: 20 Issue: 1

    • DOI

      10.1007/s11784-018-0519-4

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Characterization of sum-semicompleteness via Caristi's fixed point theorem in semimetric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Function Spaces

      Volume: 2018 Pages: 1-7

    • DOI

      10.1155/2018/9435470

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Fixed point theorem for a kind of Ciric type contractions in complete metric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Advances in the Theory of Nonlinear Analysis and its Applications

      Volume: 2 Issue: 1 Pages: 33-41

    • DOI

      10.31197/atnaa.375870

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Fixed point theorems for contractions in semicomplete semimetric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Carpathian Journal of Mathematics

      Volume: 34 Pages: 269-275

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Edelstein's fixed point theorem in semimetric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Nonlinear and Variational Analysis

      Volume: 2 Issue: 2 Pages: 165-175

    • DOI

      10.23952/jnva.2.2018.2.05

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Improvements on Bogin-type fixed point theorems in complete metric spaces2018

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Carpathian Journal of Mathematics

      Volume: 34 Pages: 425-431

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] A negative answer to Popescu's conjecture2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Fixed Point Theory

      Volume: 18 Issue: 1 Pages: 385-389

    • DOI

      10.24193/fpt-ro.2017.1.30

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Redefinition of τ-distance in metric spaces2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Function Spaces

      Volume: 2017 Pages: 1-8

    • DOI

      10.1155/2017/4168486

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Existence and approximation of fixed points of Chatterjea mappings with Bregman distances2017

    • Author(s)
      Fumiaki Kohsaka and Tomonari Suzuki
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 3 Pages: 73-86

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Fixed point theorems for Ciric type contractions and others in complete metric spaces2017

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

      Linear and Nonlinear Analysis

      Volume: 3 Pages: 111-120

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A generalization of the Banach contraction principle in noncomplete metric spaces2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Filomat

      Volume: 31 Issue: 11 Pages: 3357-3363

    • DOI

      10.2298/fil1711357s

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Basic inequality on a b-metric space and its applications2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 2017 Issue: 1

    • DOI

      10.1186/s13660-017-1528-3

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Some notes on generalizations of both Ciric's and Bogin's fixed point theorems2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Pure and Applied Functional Analysis

      Volume: 2 Pages: 677-684

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nadler's fixed point theorem in nu-generalized metric spaces2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Fixed Point Theory and Applications

      Volume: 2017 Issue: 1

    • DOI

      10.1186/s13663-017-0611-2

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The weakest contractive conditions for Edelstein's mappings to have a fixed point in complete metric spaces2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Fixed Point Theory and Applications

      Volume: 19 Issue: 4 Pages: 2361-2368

    • DOI

      10.1007/s11784-017-0430-4

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] The strongest sequentially compatible topology on a nu-generalized metric space2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Nonlinear and Variational Analysis

      Volume: 1 Pages: 333-343

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterizations of contractive conditions by using convergent sequences2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Fixed Point Theory and Applications

      Volume: 2017 Issue: 1

    • DOI

      10.1186/s13663-017-0623-y

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Every generalized metric space has a sequentially compatible topology2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 3 Pages: 393-399

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Comments on some recent existence theorems of best proximity points for Kannan-type and Chatterjea-type mappings2017

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Nihonkai Mathematical Journal

      Volume: 28 Pages: 105-116

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A direct proof of some resent generalization of both Ciric's and Bogin's fixed point theorems2017

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

      Bulletin of the Kyushu Institute of Technology

      Volume: 64 Pages: 13-19

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Journal Article] Comments on some recent generalization of the Banach contraction principle2016

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 2016 Issue: 1

    • DOI

      10.1186/s13660-016-1057-5

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Discussion of several contractions by Jachymski's approach2016

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Fixed Point Theory and Applications

      Volume: 2016 Issue: 1

    • DOI

      10.1186/s13663-016-0581-9

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Generalizations of both Ciric's and Bogin's fixed point theorems2016

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

      Journal of Nonlinear and Convex Analysis

      Volume: 17 Pages: 2183-2196

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Completeness of 3-generalized metric spaces2016

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Filomat

      Volume: 30 Issue: 13 Pages: 3575-3585

    • DOI

      10.2298/fil1613575s

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Another generalization of Edelstein's fixed point theorem in generalized metric spaces2016

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 2 Pages: 271-279

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Numbers on diameter in ν-generalized metric spaces2016

    • Author(s)
      Tomonari Suzuki
    • Journal Title

      Bulletin of the Kyushu Institute of Technology

      Volume: 63 Pages: 1-13

    • Related Report
      2016 Research-status Report
    • Open Access
  • [Presentation] 距離空間上の写像に関する縮小条件2018

    • Author(s)
      Tomonari Suzuki
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2018 Research-status Report
  • [Presentation] Recent results on contractive conditions and fixed point theory2018

    • Author(s)
      Tomonari Suzuki
    • Organizer
      The Sixth Asian Conference on Nonlinear Analysis and Optimization (NAO-Asia 2018)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 距離空間上の写像に関する縮小条件および不動点定理2018

    • Author(s)
      Tomonari Suzuki
    • Organizer
      京都大学数理解析研究所:研究集会『関数空間の一般化とその周辺』
    • Related Report
      2018 Research-status Report
  • [Presentation] nu-generalized metric space の2つの位相2018

    • Author(s)
      Tomonari Suzuki
    • Organizer
      日本数学会年会
    • Related Report
      2017 Research-status Report
  • [Presentation] tau-distance の再定義2017

    • Author(s)
      Tomonari Suzuki
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2017 Research-status Report
  • [Presentation] semimetric space についての研究2017

    • Author(s)
      Tomonari Suzuki
    • Organizer
      日本数学会九州支部例会
    • Related Report
      2017 Research-status Report
  • [Presentation] 距離空間における不動点定理2017

    • Author(s)
      Tomonari Suzuki
    • Organizer
      京都大学数理解析研究所:研究集会『関数空間の構造とその周辺』
    • Place of Presentation
      京都大学
    • Related Report
      2016 Research-status Report
  • [Presentation] Banach の縮小原理のもう1つの拡張定理2017

    • Author(s)
      Tomonari Suzuki
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京
    • Related Report
      2016 Research-status Report
  • [Presentation] ν-generalized metric space の基本的な性質2016

    • Author(s)
      Tomonari Suzuki
    • Organizer
      数理経済学会定例セミナー
    • Place of Presentation
      法政大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] ν-generalized metric space について2016

    • Author(s)
      Tomonari Suzuki
    • Organizer
      実函数論・函数解析学合同シンポジウム
    • Place of Presentation
      首都大学東京
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Ciric の不動点定理と Bogin の不動点定理2016

    • Author(s)
      Tomonari Suzuki
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      関西大学
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2025-01-30  

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