Fixed point theory and its applications

• Project/Area Number: 18740075
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kyushu Institute of Technology
• Principal Investigator: SUZUKI Tomonari Kyushu Institute of Technology, 大学院・工学研究院, 准教授 (00303173)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,800,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000); Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: 実解析 / 不動点 / 非拡大写像 / 非拡大半群 / 縮小写像 / PS条件 / τ-distance / James定数 / 均衡点 / Kannan写像

Research Abstract

この研究期間の3年間、距離空間における不動点定理、非拡大写像に対する収束定理、非拡大半群に関する不動点定理を改良することに成功した。多くの研究成果を得ることができたが、特に、論文番号10の非拡大半群に関する不動点定理は、国内外の研究者に好評であった。

Research Products

• [Journal Article] Some similarity between contractions and Kannan mappings (2008)
  • Author(s): M. Kikkawa and T. Suzuki
  • Journal Title: Fixed Point Theory and Applications 2008
  • NAID: 120002441070
  • Peer Reviewed
• [Journal Article] w-distances and tau-distances (2008)
  • Author(s): T. Suzuki
  • Journal Title: Nonlinear Functional Analysis and Applications 13 Pages: 15-27
  • Peer Reviewed
• [Journal Article] Mizoguchi-Takahashi's fixed point theorem is a real generalization of Nadler's (2008)
  • Author(s): T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 340 Pages: 752-755
  • NAID: 120002441073
  • Peer Reviewed
• [Journal Article] Fixed point theorems and convergence theorems for some generalized nonexpansive mappings (2008)
  • Author(s): T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 340 Pages: 1088-1095
  • NAID: 120002441072
  • Peer Reviewed
• [Journal Article] On the relation between the weak Palais-Smale condition and coercivity given by Zhong (2008)
  • Author(s): T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 68 Pages: 2471-2478
  • NAID: 120002441071
  • Peer Reviewed
• [Journal Article] A generalized Banach contraction principle that characterizes metric completeness (2008)
  • Author(s): T. Suzuki
  • Journal Title: Proceedings of the American Mathematical Society 136 Pages: 1861-1869
  • Peer Reviewed
• [Journal Article] Mosco convergence of the sets of fixed points for one-parameter nonexpansive semigroups (2008)
  • Author(s): T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 68 Pages: 3870-3878
  • Peer Reviewed
• [Journal Article] On the calculation of the James constant of Lorentz sequence spaces (2008)
  • Author(s): K. Mitani, K. -S. Saito and T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 343 Pages: 310-314
  • NAID: 120002441074
  • Peer Reviewed
• [Journal Article] Three fixed point theorems for generalized contractions with constants in complete metric spaces (2008)
  • Author(s): M. Kikkawa and T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 69 Pages: 2942-2949
  • Peer Reviewed
• [Journal Article] A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point (2008)
  • Author(s): T. Suzuki
  • Journal Title: Proceedings of the American Mathematical Society 136 Pages: 4089-4093
  • Peer Reviewed
• [Journal Article] Best proximity points for cyclic Meir-Keeler contractions (2008)
  • Author(s): C. Di Bari, T. Suzuki and C. Vetro
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 69 Pages: 3790-3794
  • Peer Reviewed
• [Journal Article] Browder convergence and Mosco convergence for families of nonexpansive mappings (2008)
  • Author(s): T. Suzuki
  • Journal Title: Cubo A Mathematical Journal 10 Pages: 101-108
  • Peer Reviewed
• [Journal Article] Three fixed point theorems for generalized contractions with constants in complete metric spaces (2008)
  • Author(s): M. Kikkawa, T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 69 Pages: 2942-2949
  • Peer Reviewed
• [Journal Article] Some similarity between contractions and Kannan mappings (2008)
  • Author(s): M. Kikkawa T. Suzuki
  • Journal Title: Fixed Point Theory and Applications 2008 Pages: 1-8
  • NAID: 120002441070
  • Peer Reviewed
• [Journal Article] Best proximity points for cyclic Meir-Keeler contractions (2008)
  • Author(s): C. Di Bari ; T. Suzuki ; C. Vetro
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 69 Pages: 3790-3794
  • Peer Reviewed
• [Journal Article] On the calculation of the James constant of Lorentz sequence spaces (2008)
  • Author(s): K. Mitani ; K.-S. Saito ; T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 343 Pages: 310-314
  • NAID: 120002441074
  • Peer Reviewed
• [Journal Article] Moudafi's viscosity approximations with Meir-Keeler contractions (2007)
  • Author(s): T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 325 Pages: 342-352
  • Peer Reviewed
• [Journal Article] A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings (2007)
  • Author(s): T. Suzuki
  • Journal Title: Proceedings of the American Mathematical Society 135 Pages: 99-106
  • Peer Reviewed
• [Journal Article] Browder's type convergence theorems for one-parameter semigroups of nonexpansive mappings in Banach spaces (2007)
  • Author(s): T. Suzuki
  • Journal Title: Israel Journal of Mathematics 157 Pages: 239-257
  • Peer Reviewed
• [Journal Article] Meir-Keeler contractions of integral type are still Meir-Keeler contractions (2007)
  • Author(s): T. Suzuki
  • Journal Title: International Journal of Mathematics and Mathematical Sciences 2007
  • Peer Reviewed
• [Journal Article] Fixed point theorems for more generalized contractions in complete metric spaces (2007)
  • Author(s): T. Suzuki
  • Journal Title: Demonstratio Mathematica 40 Pages: 219-227
  • Peer Reviewed
• [Journal Article] Some notes on Bauschke's condition (2007)
  • Author(s): T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 67 Pages: 2224-2231
  • Peer Reviewed
• [Journal Article] A definitive result on asymptotic contractions (2007)
  • Author(s): T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 335 Pages: 707-715
  • Peer Reviewed
• [Journal Article] Meir-Keeler contractions of integral type are still Meir-Keeler Contractions (2007)
  • Author(s): T. Suzuki
  • Journal Title: International Journal of Mathematics and Mathematical Sciences 2007 Pages: 392811-6
  • Peer Reviewed
• [Journal Article] The set of common fixed points of a one-parameter continuous semigroup of nonexpansive mappings is F(frac12 T(1) + frac12 T(sqrt2)) in strictly convex Banach spaces (2006)
  • Author(s): T. Suzuki
  • Journal Title: Taiwanese Journal of Mathematics 10 Pages: 381-397
  • Peer Reviewed
• [Journal Article] The set of common fixed points of a one-parameter continuous semigroup of mappings is F(T(1)) cap F(T(sqrt2)) (2006)
  • Author(s): T. Suzuki
  • Journal Title: Proceedings of the American Mathematical Society 134 Pages: 673-681
  • Peer Reviewed
• [Journal Article] Fixed point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces (2006)
  • Author(s): T. Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods & Applications 64 Pages: 971-978
  • Peer Reviewed
• [Journal Article] Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces (2006)
  • Author(s): T. Suzuki
  • Journal Title: Abstract and Applied Analysis 2006
  • Peer Reviewed
• [Journal Article] Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces (2006)
  • Author(s): T. Suzuki
  • Journal Title: Fixed Point Theory and Applications 2006
  • Peer Reviewed
• [Journal Article] Lou's fixed point theorem in a space of continuous mappings (2006)
  • Author(s): T. Suzuki
  • Journal Title: Journal of the Mathematical Society of Japan 58 Pages: 769-774
  • NAID: 10018381107
  • Peer Reviewed
• [Journal Article] The strong Ekeland variational principle (2006)
  • Author(s): T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 320 Pages: 787-794
  • Peer Reviewed
• [Journal Article] Common fixed points of two commuting mappings in complete metric spaces (2006)
  • Author(s): T. Suzuki, R. Saadati and D. O'Regan
  • Journal Title: Bulletin of the Iranian Mathematical Society 32 Pages: 53-66
  • Peer Reviewed
• [Journal Article] Characterizations of common fixed points of one-parameter nonexpansive semigroups, and convergence theorems to common fixed points (2006)
  • Author(s): T. Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 324 Pages: 1006-1019
  • Peer Reviewed
• [Journal Article] Common fixed points of one-parameter nonexpansive semigroups (2006)
  • Author(s): T. Suzuki
  • Journal Title: The Bulletin of the London Mathematical Society 38 Pages: 1009-1018
  • Peer Reviewed
• [Journal Article] The set of common fixed points of a one-parameter continuous semigroup of mappings is F(T(1)) cap F(T(sqrt2)) (2006)
  • Author(s): T.Suzuki
  • Journal Title: Proceedings of the American Mathematical Society 134 Pages: 673-681
• [Journal Article] Fixed point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces (2006)
  • Author(s): T.Suzuki
  • Journal Title: Nonlinear Analysis, Theory, Methods ＆ Applications 64 Pages: 971-978
• [Journal Article] Lou's fixed point theorem in a space of continuous mappings (2006)
  • Author(s): T.Suzuki
  • Journal Title: Journal of the Mathematical Society of Japan 58 Pages: 769-774
  • NAID: 10018381107
• [Journal Article] The strong Ekeland variational principle (2006)
  • Author(s): T.Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 320 Pages: 787-794
• [Journal Article] Characterizations of common fixed points of one-parameter nonexpansive semigroups, and convergence theorems to common fixed points (2006)
  • Author(s): T.Suzuki
  • Journal Title: Journal of Mathematical Analysis and Applications 324 Pages: 1006-1019
• [Journal Article] Common fixed points of one-parameter nonexpansive semigroups (2006)
  • Author(s): T.Suzuki
  • Journal Title: The Bulletin of the London Mathematical Society 38 Pages: 1009-1018
• [Presentation] Halpern's convergence for nonexpansive mappings (2009)
  • Author(s): T. Suzuki
  • Organizer: The Sixth International Conference on Nonlinear Analysis and Convex Analysis (NACA 2009)
  • Place of Presentation: 東京工業大学
  • Year and Date: 2009-03-30
• [Presentation] 非拡大写像が不動点を持つことvs非拡大半群が共通不動点持つこと (2008)
  • Author(s): T. Suzuki
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-27
• [Presentation] FPP for nonexpansive mappings vs that for nonexpansive semigroups (2008)
  • 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: 2008-09-02
• [Presentation] Ekelandの$\varepsion$変分不等式 (2008)
  • Author(s): T. Suzuki
  • Organizer: 研究集会「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: 2008-06-05
• [Presentation] 非拡大半群等の不動点に関するここ4年間の結果 (2007)
  • Author(s): 鈴木 智成
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-22
• [Presentation] Meir-Keeler縮小写像とL関数 (2007)
  • Author(s): 鈴木 智成
  • 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: 2007-09-04
• [Presentation] Recent results concerning fixed point sets for nonexpansive semigroups (2007)
  • Author(s): T. Suzuki
  • Organizer: The 8th International Conference on Fixed Point Theory and its Applications (ICFPTA 2007)
  • Place of Presentation: チェンマイ大学(タイ)
  • Year and Date: 2007-07-21
• [Presentation] 弱Palais-Smale条件とcoercivity (2007)
  • Author(s): 鈴木 智成
  • Organizer: 研究集会「バナッハ空間、関数空間及び不等式の研究とその応用」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-06-08
• [Presentation] Recent results concerning common fixed points of one-parameter nonexpansive semigroups
  • Author(s): T. Suzuki
  • Organizer: The Second International Symposium on Banach and Function Spaces 2006(ISBFS 2006)
• [Presentation] 非拡大半群の共通不動点に関する最近の結果
  • Author(s): T. Suzuki
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] 非拡大半群の共通不動点に関する最近の結果
  • Author(s): T. Suzuki
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] Recent results concerning fixed point sets for nonexpansive semigroups
  • Author(s): T. Suzuki
  • Organizer: The 8th International Conference on Fixed Point Theory and its Applications(ICFPTA 2007)
• [Presentation] 非拡大半群等の不動点に関するここ4年間の結果
  • Author(s): T. Suzuki
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] 非拡大写像が不動点を持つことvs非拡大半群が共通不動点持つこと
  • Author(s): T. Suzuki
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] Generalizations of Kannan's fixed point theorem
  • Author(s): M. Nakanishi and T. Suzuki
  • Organizer: The Sixth International Conference on Nonlinear Analysis and Convex Analysis(NACA 2009)
• [Presentation] Halpern's convergence for nonexpansive mappings
  • Author(s): T. Suzuki
  • Organizer: The Sixth International Conference on Nonlinear Analysis and Convex Analysis(NACA 2009)