Abstract
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.
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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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Journal
Studia Universitatis Babeş-Bolyai, Mathematica
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Universitatea ”Babeș-Bolyai” Cluj-Napoca
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References
[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.