Continuous dependence on parameters of the fixed points set for some set-valued operators

• Autorzy: Eduard Kirr , Adrian Petruel
• Języki publikacji: EN

Abstrakty

EN

In this paper we extend the notion of I⁰-continuity and uniform I⁰-continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators.

Słowa kluczowe

EN

I⁰-continuity; semi-continuous set-valued operators; Hausdorff-Pompeiu generalized semi-metric; contractive type set-valued operators

Kategorie tematyczne

• 47H04: Set-valued operators
• 47H10: Fixed-point theorems
• 34A60: Differential inclusions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1997
• Tom: 17
• Numer: 1-2
• Strony: 29-41

Daty

wydano

1997

otrzymano

1997-09-11

poprawiono

1998-02-22

Twórcy

autor

Eduard Kirr

• Babe-Bolyai University, Department of Mathematics, str. M. Koglniceanu nr.1, 3400 Cluj-Napoca, Romania

autor

Adrian Petruel

• Babe-Bolyai University, Department of Mathematics, str. M. Koglniceanu nr.1, 3400 Cluj-Napoca, Romania

Bibliografia

• [1] E. Barcz, Some fixed points theorems for multi-valued mappings, Demonstratio Math. Vol. XVI, 3 (1983), 725-743.
• [2] I. Del Prete and C. Esposito, Elementi uniti di transformazioni funzionali e teoremi di dipendenza continua, Rend. Circ. Mat. di Palermo serie 2, 23 (1974), 187-205.
• [3] J.Dugundji, Topology, Allyn and Bacon Inc., Boston, 1966.
• [4] E. Kirr, On continuous dependence on parameters of the fixed point set for some classes of metric operators, to appear.
• [5] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ., Dordrecht, 1991.
• [6] A.I. Rus, Generalized contraction, Univ. Cluj-Napoca Preprint, 3 (1983), 1-130.
• [7] R.E. Smithson, Fixed points for contractive multifunctions, Proc. A.M.S., 27 (1971), 192-194.
• [8] R. Wegrzyk, Fixed-point theorems for multi-valued functions and their applications to functional equations, Diss. Math., 201 (1982), 1-31.