Fixed Point Theory and Related Nonlinear Problems

• Project/Area Number: 21540189
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu 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): KATO Mikio 信州大学, 工学部, 教授 (50090551) ; KIKKAWA Misako 埼玉大学, 理工学研究科, 非常勤講師 (20444052) ; 仙葉 隆 九州工業大学, 工学(系)研究科(研究院), 教授 (30196985)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 実解析 / 不動点理論 / 不動点 / 非線形半群 / 自己稠密核 / 非拡大写像 / 非拡大写像族 / 縮小写像 / Kannan写像 / Banach空間の幾何学 / 非拡大半群 / τ-distance / 回帰性 / 一様non-1^n_1性

Research Abstract

In these four years, we have obtained several results in fixed point theory. For example, we have obtained the best possible condition on some type of Browder's convergence for nonexpansive semigroups in Hilbert spaces. We have discussed the concept of generalized nonexpansive mappings in Banach spaces and successive approximation converging to a fixed point in complete metric spaces.

Research Products

• [Journal Article] Browder's convergence for one-parameter nonexpansive semigroups (2012)
  • Author(s): S. Akiyama & T. Suzuki
  • Journal Title: anadian Mathematical Bulletin Volume: 55 Pages: 15-25
  • Peer Reviewed
• [Journal Article] Browder's convergence for one-parameter nonexpansive semigroups (2012)
  • Author(s): Shigeki Akiyama, Tomonari Suzuki
  • Journal Title: Canadian Mathematical Bulletin Volume: 55 Issue: 1 Pages: 15-25
  • DOI: 10.4153/cmb-2011-071-9
  • Peer Reviewed
• [Journal Article] Fixed point theory for a class of generalized nonexpansive mappings (2011)
  • Author(s): J. Garcia Falset, E. Llorens Fuster & T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 375 Pages: 185-195
  • Peer Reviewed
• [Journal Article] A simple proof of a Browder's type convergence theorem for infinite families of nonexpansive mappings in Banach spaces (2011)
  • Author(s): T.Suzuki
  • Journal Title: Proceedings of the Third International Symposium on Banach and Function Spaces Volume: 3 Pages: 305-316
  • Peer Reviewed
• [Journal Article] An extension of some Kannan-type fixed point theorem involving constants (2011)
  • Author(s): M.Nakanishi, T.Suzuki
  • Journal Title: Proceedings of the Third International Symposium on Banach and Function Spaces Volume: 3 Pages: 431-440
  • Peer Reviewed
• [Journal Article] An easily verifiable proof of the Brouwer fixed point theorem (2011)
  • Author(s): Y.Takeuchi, T.Suzuki
  • Journal Title: Bulletin of the Kyushu Institute of Technology Volume: 3 Pages: 1-5
  • NAID: 120005257247
• [Journal Article] On the inequality C_NJ(X)≦J(X) (2011)
  • Author(s): Y.Takahashi, M.Kato
  • Journal Title: Proceedings of the Third International Symposium on Banach and Function Spaces Volume: 3 Pages: 317-328
  • Peer Reviewed
• [Journal Article] On the well posedness of a class of PDEs including porous medium and chemotaxis effect (2011)
  • Author(s): M.Efendiev; T.Senba
  • Journal Title: Advances in Differential Equations Volume: 16 Pages: 937-954
  • Peer Reviewed
• [Journal Article] A sufficient condition for type I blowup in a parabolic-elliptic system (2011)
  • Author(s): N.Mizoguchi, T.Senba
  • Journal Title: Journal of Differential Equations Volume: 250 Pages: 182-203
  • Peer Reviewed
• [Journal Article] Almost biased mappings and almost compatible mappings are equivalent under some condition (2010)
  • Author(s): T. Suzuki & H. K. Pathak
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 368 Pages: 211-217
  • Peer Reviewed
• [Journal Article] Characterizations of reflexivity and compactness via the strong Ekeland variational principle (2010)
  • Author(s): T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications Volume: 72 Pages: 2204-2209
  • Peer Reviewed
• [Journal Article] Three existence theorems for weak contractions of Matkowski type (2010)
  • Author(s): T. Suzuki & C. Vetro
  • Journal Title: International Journal of Mathematics and Statistics Volume: 6 Pages: 110-120
  • Peer Reviewed
• [Journal Article] Convergence of the sequence of successive approximations to a fixed point (2010)
  • Author(s): T. Suzuki
  • Journal Title: Fixed Point Theory and Applications Volume: Article ID 716971 Pages: 1-14
  • Peer Reviewed
• [Journal Article] An observation on Kannan mappings (2010)
  • Author(s): M. Nakanishi & T. Suzuki
  • Journal Title: Central European Journal of Mathematics Volume: 8 Pages: 170-178
  • Peer Reviewed
• [Journal Article] Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces (2010)
  • Author(s): G. Lopez & T. Suzuki
  • Journal Title: Fixed Point Theory and Applications Volume: Article ID 418030 Pages: 1-8
  • Peer Reviewed
• [Journal Article] Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces (2010)
  • Author(s): G.Lopez Acedo ; T.Suzuki
  • Journal Title: Fixed Point Theory and Applications Volume: 2010 Pages: 418030-418030
  • Peer Reviewed
• [Journal Article] Convergence of the sequence of successive approximations to a fixed point (2010)
  • Author(s): T.Suzuki
  • Journal Title: Fixed Point Theory and Applications Volume: 2010 Pages: 716971-716971
  • Peer Reviewed
• [Journal Article] Browder's convergence for (uniformly asymptotically regular) one-parameter nonexpansive semigroups in Banach spaces (2010)
  • Author(s): G.Lopez Acedo ; T.Suzuki
  • Journal Title: Proceedings of the Ninth International Conference on Fixed Point Theory and its Applications Pages: 131-143
  • Peer Reviewed
• [Journal Article] A fixed point theorem for some Kannan-type set-valued mappings (2010)
  • Author(s): M.Nakanishi ; T.Suzuki
  • Journal Title: Proceedings of the Sixth International Conference on Nonlinear Analysis and Convex Analysis Pages: 249-255
  • Peer Reviewed
• [Journal Article] Wittmann's convergence theorem for nonexpansive mappings (2010)
  • Author(s): T.Suzuki
  • Journal Title: Proceedings of the Sixth International Conference on Nonlinear Analysis and Convex Analysis Pages: 327-339
  • Peer Reviewed
• [Journal Article] On sharp estimates concerning the von Neumann-Jordan and James constants for a Banach space (2010)
  • Author(s): M.Kato, Y.Takahashi
  • Journal Title: Rend.Circ.Mat.Palermo Serie II Suppl. Volume: 82 Pages: 75-91
  • Peer Reviewed
• [Journal Article] A new type of fixed point theorem in metric spaces (2009)
  • Author(s): T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications Volume: 71 Pages: 5313-5317
  • Peer Reviewed
• [Journal Article] The existence of best proximity points in metric spaces with the property UC (2009)
  • Author(s): T. Suzuki, M. Kikkawa & C. Vetro
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications Volume: 71 Pages: 2918-2926
  • Peer Reviewed
• [Journal Article] Subrahmanyam's fixed point theorem (2009)
  • Author(s): T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications Volume: 71 Pages: 1678-1683
  • Peer Reviewed
• [Journal Article] Fixed point property for nonexpansive mappings versus that for nonexpansive semigroups (2009)
  • Author(s): T.Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 70 Pages: 3358-3361
  • NAID: 120002441545
  • Peer Reviewed
• [Journal Article] Reich's problem concerning Halpern's convergence (2009)
  • Author(s): T.Suzuki
  • Journal Title: Archiv der Mathematik 92 Pages: 602-613
  • Peer Reviewed
• [Journal Article] A generalization of Kannan's fixed point theorem (2009)
  • Author(s): Y.Enjouji ; M.Nakanishi ; T.Suzuki
  • Journal Title: Fixed Point Theory and Applications 2009
  • Peer Reviewed
• [Journal Article] Subrahmanyam's fixed point theorem (2009)
  • Author(s): T.Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 71 Pages: 1678-1683
  • Peer Reviewed
• [Journal Article] The existence of best proximity points in metric spaces with the property UC (2009)
  • Author(s): T.Suzuki ; M.Kikkawa ; C.Vetro
  • Journal Title: Nonlinear Analysis, Theory Methods & Applications 71 Pages: 2918-2926
  • Peer Reviewed
• [Journal Article] A new type of fixed point theorem in metric spaces (2009)
  • Author(s): T.Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 71 Pages: 5313-5317
  • Peer Reviewed
• [Journal Article] Uniform non-l^n_1-ness of l_∞-sums of Banach spaces (2009)
  • Author(s): M.Kato ; T.Tamura
  • Journal Title: Commentationes Mathematicae. Prace Matematyczne. 49 Pages: 179-187
  • Peer Reviewed
• [Presentation] Banach 空間の回帰性と強 Ekeland $￥varepsilon$変分不等式 (2013)
  • Author(s): T. Suzuki
  • Organizer: 日本数学会年会
  • Place of Presentation: 慶應義塾大学(横浜)
  • Year and Date: 2013-03-26
• [Presentation] Some examples on $p$-uniform convexity and $q$-uniform smoothness (2012)
  • Author(s): T. Suzuki
  • Organizer: The Fourth International Symposium on Banach and Function Spaces 2012 (ISBFS 2009)
  • Place of Presentation: 九州工業大学(北九州)
  • Year and Date: 2012-09-15
• [Presentation] Brouwerの不動点定理の初等的な証明 (2011)
  • Author(s): Y.Takeuchi, T.Suzuki
  • Organizer: 実解析学シンポジウム
  • Place of Presentation: 信州大学
  • Year and Date: 2011-11-05
• [Presentation] 不動点定理に関するここ数年の結果 (2011)
  • Author(s): Tomonari Suzuki
  • Organizer: 日本数学会九州支部例会
  • Place of Presentation: 熊本大学
  • Year and Date: 2011-10-22
• [Presentation] compatible mappings について (2011)
  • Author(s): T. Suzuki
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学(松本)
  • Year and Date: 2011-09-28
• [Presentation] compatible mappingsについて (2011)
  • Author(s): Tomonari Suzuki
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-28
• [Presentation] Ishikawa's convergence theorem for finite families of nonexpansive mappings (2011)
  • Author(s): Tomonari Suzuki
  • Organizer: 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: 2011-08-30
• [Presentation] MatkowskiによるBanachの縮小原理の拡張定理とBoyd-Wongによる拡張定理の違い (2011)
  • Author(s): T.Suzuki
  • Organizer: 研究集会「バナッハ空間論の研究とその周辺」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-02-15
• [Presentation] Various fixed point theorems in metric spaces (2010)
  • Author(s): T.Suzuki
  • Organizer: 実解析学シンポジウム 2010
  • Place of Presentation: 九州工業大学
  • Year and Date: 2010-11-14
• [Presentation] 非拡大半群のBrowder収束と係数条件 (2010)
  • Author(s): T.Suzuki
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-29
• [Presentation] 非拡大半群のBrowder収束と係数条件 (2010)
  • Author(s): T. Suzuki
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学(名古屋)
  • Year and Date: 2010-09-24
• [Presentation] Various generalizations of the Banach contraction principle (2010)
  • Author(s): T. Suzuki
  • Organizer: The second Asian Conference on Nonlinear Analysis and Optimization (NAO-Asia 2010)
  • Place of Presentation: Royal Paradise Hotel & Spa (Phuket, Thailand)
  • Year and Date: 2010-09-11
• [Presentation] Various generalizations of the Banach contraction principle (2010)
  • Author(s): T.Suzuki
  • Organizer: The second Asian Conference on Nonlinear Analysis and Optimization
  • Place of Presentation: Phuket(Thailand)(招待講演)
  • Year and Date: 2010-09-11
• [Presentation] Recent extensions of the Banach contraction principle (2010)
  • Author(s): T.Suzuki
  • Organizer: 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: 2010-08-30
• [Presentation] Banach空間の回帰性と強Ekeland ε変分不等式 (2010)
  • Author(s): T.Suzuki
  • Organizer: 日本数学会年会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2010-03-26
• [Presentation] Banachの縮小原理の2つの拡張定理 (2009)
  • Author(s): T. Suzuki
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学(豊中)
  • Year and Date: 2009-09-24
• [Presentation] Banachの縮小原理の2つの拡張定理 (2009)
  • Author(s): T.Suzuki
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] Observations on Kannan mappings (2009)
  • Author(s): M. Nakanishi & T. Suzuki
  • Organizer: The Third International Symposium on Banach and Function Spaces 2009 (ISBFS 2009)
  • Place of Presentation: 九州工業大学(北九州)
  • Year and Date: 2009-09-17
• [Presentation] The Ekeland variational principle characterizes some properties of underlying spaces (2009)
  • Author(s): T. Suzuki
  • Organizer: The Third International Symposium on Banach and Function Spaces 2009 (ISBFS 2009)
  • Place of Presentation: 九州工業大学(北九州)
  • Year and Date: 2009-09-15
• [Presentation] The Ekeland variational principle characterizes some properties of underlying spaces (2009)
  • Author(s): T.Suzuki
  • Organizer: The Third International Symposium on Banach and Function Spaces 2009
  • Place of Presentation: 九州工業大学
  • Year and Date: 2009-09-15
• [Presentation] Recent results concerning convergence theorems for nonexpansive mappings and families of nonexpansive mappings (2009)
  • Author(s): T. Suzuki
  • Organizer: the 9th International Conference on Fixed Point Theory and its Applications (ICFPTA2009)
  • Place of Presentation: National Changhua University of Education (Changhua, Taiwan)
  • Year and Date: 2009-07-19
• [Presentation] Recent results concerning convergence theorems for nonexpansive mappings and families of nonexpansive mappings (2009)
  • Author(s): T.Suzuki
  • Organizer: The 9th International Conference on Fixed Point Theory and its Applications
  • Place of Presentation: Changhua(Taiwan)
  • Year and Date: 2009-07-19
• [Presentation] 非拡大半群のBrowder収束 (2009)
  • Author(s): T.Suzuki
  • Organizer: 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: 2009-05-21
• [Presentation] Some examples on p-uniform convexity and q-uniform smoothness
  • Author(s): Tomonari Suzuki
  • Organizer: The Fourth International Symposium on Banach and Function Spaces 2012
  • Place of Presentation: 九州工業大学
• [Book] Banach and Function Spaces III (2011)
  • Author(s): M. Kato, Lech Maligranda & T. Suzuki
  • Total Pages: 437
  • Publisher: Yokohama Publishers
• [Book] Proceedings of the Third International Symposium on Banach and Function Spaces III (2011)
  • Author(s): Mikio Kato; Lech Maligranda; Tomonari Suzuki
  • Total Pages: 473
  • Publisher: Yokohama Publishers