Note on an abstract continuation theorem


The author shows that one may derive the property of homotopy invariance for the fixed point index (for compact maps for open bounded sets in Banach spaces) and Granas’ topological transversality theorem from a form of the continuation principle which he obtained earlier [“Sur un principe topologique”, Preprint No. 6, 163–168, Fac. Mat., “Babeş-Bolyai” Univ. Cluj-Napoca, Cluj-Napoca, 1991; per bibl.; Nonlinear Anal. 20 (1993), no. 1, 1–9;


Radu Precup
Babeş-Bolyai University, Cluj-Napoca, Romania


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R. Precup, Note on an abstract continuation theorem, Studia Univ. Babeş-Bolyai Math., 37 (1992) no. 2, 85-90.


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Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania


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MR: 95m:58018.

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[2] A. Granas, Homotopy extension theorem in Banach spaces and some of its applications to the theory of non-linear equations, Bull. Acad. Polon. Sci. 7 (2959), 387-394.
[3] R. Precup, Topological transversality, perturbation theorems and second order differential equations, Preprint nr. 3(1989), ”Babeș-Bolyai” Univ,, Fac. of Math., 149-1264.
[4] R. Precup, Generalized topological transverslity and mappings of monotone type, Studia Universitatis ”Babeș-Bolyai” 35(1990), 44-50.
[5] R. Precup, Generalized topological transverslity and existence theorems, Libertas Mathematica 11(1991), 65-79.
[6] R. Precup, Sur un principe topologique, Preprint nr. 6(1991), ”Babeș-Bolyai” Univ., Fac. of Math., 163-168.
[7] R. Precup, Topological transversality and boundary  problems for second order functional differential equations, in Differential Equations and Control Theory (V.  Barbu ed.), Logman Scientific & Technical, 1991, 283-288
[8] R. Precup, On the topological transversality principle, Nonlinear Analysis, Theory, Methods & Applicaitons, 20(1993), in print.
[9] R. Precup, On a topological principle II, Preprint nr.6(1992), ”Babeș-Bolyai” Univ., Fac. of Math., in print.
[10] V. Lakshmikantham, Young Sun, A theorem on the existence of two fixed points, Journal of Mathematical and Physical Sciences 25(1991) 281-286.

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