×

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 J. S. Bae [J. Math. Anal. Appl. 284, 690–697 (2003; Zbl 1033.47038)] and others.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 1033.47038
PDF BibTeX XML Cite
Full Text: DOI

References:

[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) · JFM 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, (), 74-83
[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 τ-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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.