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We generalize Suzuki’s fixed point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces.
Wydawca
Czasopismo
Rocznik
Tom
Strony
219--227
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Department of Mathematics Kyushu Institute of Technology Sensuicho, Tobata, Kitakyushu 804-8550, Japan, suzuki-t@mns.kyutech.ac.jp
Bibliografia
- [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133-181.
- [2] J. Caristi and W. A. Kirk, Geometric fixed point theory and inwardness conditions, Lecture Notes in Math., Vol. 490, pp. 74-83, Springer, Berlin, 1975.
- [3] Lj. B. Ći rić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267-273.
- [4] M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc. 12 (1961), 7-10.
- [5] M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74-79.
- [6] I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443-474.
- [7] O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon. 44 (1996), 381-391.
- [8] W. A. Kirk, Contraction mappings and extensions in Handbook of metric fixed point theory (W. A. Kirk and B. Sims Eds.), 2001, pp. 1-34, Kluwer Academic Publishers, Dordrecht.
- [9] W. A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. 277 (2003), 645-650.
- [10] T. C. Lim, On characterizations of Meir-Keeler contractive maps, Nonlinear Anal. 46 (2001), 113-120.
- [11] A. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326-329.
- [12] S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488.
- [13] P. V. Subrahmanyam, Remarks on some fixed point theorems related to Banach's contraction principle, J. Math. Phys. Sci. 8 (1974), 445-457.
- [14] T. Suzuki, Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl. 253 (2001), 440-458.
- [15] T. Suzuki, On Downing-Kirk's theorem, J. Math. Anal. Appl. 286 (2003), 453-458.
- [16] T. Suzuki, Several fixed point theorems concerning _ -distance, Fixed Point Theory Appl. 2004 (2004), 195-209.
- [17] T. Suzuki, Contractive mappings are Kannan mappings, and Kannan mappings are contractive mappings in some sense, Comment. Math. Prace Mat. 45 (2005), 45-58.
- [18] T. Suzuki, Fixed point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Nonlinear Anal. 64 (2006), 971-978.
- [19] T. Suzuki, Some notes on Meir-Keeler contractions and L-functions, Bull. Kyushu Inst. Technol. 53 (2006), 1-13.
- [20] D. Tataru, Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms, J. Math. Anal. Appl. 163 (1992), 345-392.
- [21] C.-K. Zhong, On Ekeland's variational principle and a minimax theorem, J. Math. Anal. Appl. 205 (1997), 239-250.
- [22] C.-K. Zhong, A generalization of Ekeland's variational principle and application to the study of the relation between the weak P.S. condition and coercivity, Nonlinear Anal. 29 (1997), 1421-1431.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0033-0022