Extension of Caristi’s fixed point theorem to vector valued metric spaces. (English) Zbl 1231.54017

Summary: The paper deals with the classical Caristi fixed point theorem in vector valued metric spaces. The results obtained seem to be new in this setting.


54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] Brønsted, A., Fixed point and partial orders, Proc. amer. math. soc., 60, 365-366, (1976)
[2] Caristi, J., Fixed point theorems for mappings satisfying inwardness conditions, Trans. amer. math. soc., 215, 241-251, (1976) · Zbl 0305.47029
[3] Caristi, J., Fixed point theory and inwardness conditions, Appl. nonlinear anal., 479-483, (1979)
[4] Halpern, B.; Bergman, G., A fixed point theorem for inward and outward maps, Trans. amer. math. soc., 130, 353-358, (1968) · Zbl 0153.45602
[5] F.E. Browder, On a theorem of Caristi and Kirk, in: Proc. Seminar on Fixed Point Theory and Its Applications, Dalhousie University, June 1975, Academic Press, pp. 23-27.
[6] Kirk, W.A.; Caristi, J., Mapping theorems in metric and Banach spaces, Bull. L’acad. polon. sci., 25, 891-894, (1975) · Zbl 0313.47041
[7] Ekeland, I., Sur LES problemes variationnels, C. R. acad. sci. Paris, 275, 1057-1059, (1972) · Zbl 0249.49004
[8] Sullivan, F., A characterization of complete metric spaces, Proc. amer. math. soc., 85, 345-346, (1981) · Zbl 0468.54021
[9] Agarwal, R.P., Contraction and approximate contraction with an application to multi-point boundary value problems, J. comput. appl. math., 9, 315-325, (1983) · Zbl 0546.65060
[10] Urabe, M., An existence theorem for multi-point boundary value problems, Funkcial. ekvac., 9, 43-60, (1966) · Zbl 0168.06502
[11] Bernfeld, S.R.; Lakshmikantham, V., An introduction to nonlinear boundary value problems, (1974), Academic Press New York · Zbl 0286.34018
[12] Suzuki, T., Generalized caristi’s fixed point theorems by bae and others, J. math. anal. appl., 302, 502-508, (2005) · Zbl 1059.54031
[13] Khamsi, M.A., Remarks on caristi’s fixed point theorem, Nonlinear anal., 71, 227-231, (2009) · Zbl 1175.54056
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