Fixed point theorems for multivalued mappings. (English) Zbl 0608.47063

Haščák, Alexander

Czech. Math. J. 35(110), 533-542 (1985).

The author generalizes a fixed point theorem of M. Švec [Arch. Math. Brno 2, 43-55 (1966; Zbl 0216.410)] to the multi-valued mappings.

Reviewer: Ioan A.Rus

MSC:

47H10

Fixed-point theorems

Keywords:

upper q-continuity; multi-valued differential systems; fixed point theorem; multi-valued mappings

Citations:

Zbl 0216.410

References:

[1]	L. Collatz: Funktionalanalysis un Numerische Mathematik. Springer-Verlag 1969. · Zbl 0139.09802
[2]	Ku Fan: Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Mat. Acad. Sci., U.S.A., 38 (1952), 121-126. · Zbl 0047.35103
[3]	A. Haščák: Integral equivalence of multi-valued differential systems. Acta Mathematica Universitatis Comeniae, Bratislava · Zbl 0645.34034
[4]	F. Riesz B. Sz.-Nagy: Leçons d’analyse fonctionnelle. Budapest 1972. · Zbl 0064.35404
[5]	W. Sobieszek: On the point-to-set mappings and functions maximum related to them. Demonstratio mathematica, Vol. VII, No. 4, (1974), 483-494. · Zbl 0356.54018
[6]	W. Sobieszek P. Kowalski: On the different definitions of the lower semicontinuity, upper semicontinuity, upper semicompacity, closity and continuity of the point-to-set maps. Demonstratio mathematica, Vol. XI, No. 4, (1978), 1053-1063. · Zbl 0408.54001
[7]	M. Švec: Fixpunktsatz und monotone Lösungen der Differentialgleichung \(y^{(n)}+B(x,y,y^{\prime}, \cdots,y^{(n-1)})y=0\). Archivum mathematicum (Brno), T. 2. (1966), 43 - 55. · Zbl 0216.41003
[8]	A. Haščák: Integral equivalence of multivalued differential systems II. Colloquia Math. Soc. J. Bolyai. 47, Differential Equations: Qualitative Theory, Szeged (Hungary), 1984. · Zbl 0645.34034