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Generalized Caristi’s fixed point theorems by Bae and others. (English) Zbl 1059.54031
Summary: We extend the generalized Caristi’s fixed point theorems proved by {\it J. S. Bae} [J. Math. Anal. Appl. 284, 690--697 (2003; Zbl 1033.47038)] and others.

54H25Fixed-point and coincidence theorems in topological spaces
Full Text: DOI
[1] Bae, J. S.: Fixed point theorems for weakly contractive multivalued maps. J. math. Anal. appl. 284, 690-697 (2003) · Zbl 1033.47038
[2] Bae, J. S.; Cho, E. W.; Yeom, S. H.: A generalization of the caristi -- kirk fixed point theorem and its applications to mapping theorems. J. korean math. Soc. 31, 29-48 (1994) · Zbl 0842.47035
[3] Banach, S.: Sur LES opérations dans LES ensembles abstraits et leur application aux équations intégrales. Fund. math. 3, 133-181 (1922) · Zbl 48.0201.01
[4] Caristi, J.: Fixed point theorems for mappings satisfying inwardness conditions. Trans. amer. Math. soc. 215, 241-251 (1976) · Zbl 0305.47029
[5] Caristi, J.; Kirk, W. A.: Geometric fixed point theory and inwardness conditions. Lecture notes in math. 490, 74-83 (1975) · Zbl 0315.54052
[6] Downing, D.; Kirk, W. A.: A generalization of caristi’s theorem with applications to nonlinear mapping theory. Pacific J. Math. 69, 339-346 (1977) · Zbl 0357.47036
[7] Ekeland, I.: On the variational principle. J. math. Anal. appl. 47, 324-353 (1974) · Zbl 0286.49015
[8] Ekeland, I.: Nonconvex minimization problems. Bull. amer. Math. soc. 1, 443-474 (1979) · Zbl 0441.49011
[9] Kada, O.; Suzuki, T.; Takahashi, W.: Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Math. japon. 44, 381-391 (1996) · Zbl 0897.54029
[10] Shioji, N.; Suzuki, T.; Takahashi, W.: Contractive mappings, kannan mappings and metric completeness. Proc. amer. Math. soc. 126, 3117-3124 (1998) · Zbl 0955.54009
[11] Suzuki, T.: Several fixed point theorems in complete metric spaces. Yokohama math. J. 44, 61-72 (1997) · Zbl 0882.47039
[12] Suzuki, T.: Generalized distance and existence theorems in complete metric spaces. J. math. Anal. appl. 253, 440-458 (2001) · Zbl 0983.54034
[13] Suzuki, T.: On downing -- kirk’s theorem. J. math. Anal. appl. 286, 453-458 (2003) · Zbl 1042.47036
[14] T. Suzuki, Several fixed point theorems concerning \tau -distance, Fixed Point Theory Appl., in press · Zbl 1076.54532
[15] T. Suzuki, Contractive mappings are Kannan mappings, and Kannan mappings are contractive mappings in some sense, submitted for publication · Zbl 1098.54024
[16] Suzuki, T.; Takahashi, W.: Fixed point theorems and characterizations of metric completeness. Topol. methods nonlinear anal. 8, 371-382 (1996) · Zbl 0902.47050
[17] Tataru, D.: Viscosity solutions of Hamilton -- Jacobi equations with unbounded nonlinear terms. J. math. Anal. appl. 163, 345-392 (1992) · Zbl 0757.35034
[18] Weston, J. D.: A characterization of metric completeness. Proc. amer. Math. soc. 64, 186-188 (1977) · Zbl 0368.54007
[19] Zhong, C. -K.: On Ekeland’s variational principle and a minimax theorem. J. math. Anal. appl. 205, 239-250 (1997) · Zbl 0870.49015