Continuation theorems for maps of Caristi type


In this paper we prove some continuation theorems for mappings of Caristi type. Our results generalize Caristi’s fixed point theorem and the continuation theorem for contractions.


Radu Precup
Babes-Bolyai University




Cite this paper as:

R. Precup, Continuation theorems for maps of Caristi type, Studia Univ. Babeş-Bolyai Math., 41 (1996) no. 4, 101-106.

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Studia Universitatis Babeş-Bolyai, Mathematica

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Universitatea ”Babeș-Bolyai” Cluj-Napoca


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[1] J. Caristi, Fixed point theorems for mappings satisfying inwardness condition, Trans. Amer. Math. Soc. 215 (1976), 241-251.
[2] M. Frigon, A. Granas, Resultats du type de leray-Schauder pour des contractions  multivoques, Topol. Methods Nonlinear Anal.4 (1994), 197-208.
[3] A. Granas, Continuation method for contractive maps, Topol. Methods Nonlinear anal. 3 (1994), 375-379.
[4] J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, Berlin, 1989.
[5] R. Precup, On the continuation principle for nonexpansive maps, Studia Univ. Babes-Bolyai/Mathematica 41, no.3 (1996), in print.
[6] R. Precup, Existence theorems for nonlinear by continuationmethods, in Proceedings of the Second World Congress of Nonlinear Analysis, Athena, Grecee, July 10-17, 1996 (ed. V. Lakshmikantham), Elsevier Science, to apppear.
[7] I.A. Rus, Metrical Fixed Point Theorem, Univ. of Cluj, Cluj, 1979.


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