Continuous selections and approximations in α-convex metric spaces

• Autorzy: A. Kowalska
• Języki publikacji: EN

Abstrakty

EN

In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.

Słowa kluczowe

EN

generalized convexity; selections; relative selections; graph-approximations

Kategorie tematyczne

• 54C60: Set-valued maps
• 54C20: Extension of maps
• 54C65: Selections

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2007
• Tom: 27
• Numer: 2
• Strony: 265-294

Daty

wydano

2007

otrzymano

2006-01-09

Twórcy

autor

A. Kowalska

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] H. Ben-El-Mechaiekh and W. Kryszewski, Equilibria of set-valued maps onnonconvex domains, Trans. Amer. Math. Soc. 349 (1997), 4159-4179.
• [2] F.S. de Blasi, L. Górniewicz and G. Pianigiani, Fixed point index for multivaled mappngs in convex metric spaces, private communication.
• [3] F.S. de Blasi and G. Pianigiani, Approximate selections in α-convex metric spaces and topological degree, Topol. Methods Nonlinear Anal. 24 (2) (2004), 347-375.
• [4] F.S. de Blasi and G. Pianigiani, Continuous selections in α-convex metric spaces, Bull. Poll. Acad. Sci. Math. 52 (3) (2004), 303-317.
• [5] F.S. de Blasi and G. Pianigiani, Pseudo-barycenters and approximations of multifunctions in metric spaces, submitted.
• [6] K. Borsuk, Theory of retracts, Monografie Matematyczne 44, Warszawa, 1967.
• [7] A. Cellina, A further result on the approximation of set-valued mapping, Atti Accad. Naz. Licei Rend. Cl. Sci. Fis. Mat. Natur. 48 (8) (1970), 412-416.
• [8] G. Colombo and V. Goncharov, Continuous selections via geodesics, Topol. Methods Nonlinear Anal. 18 (1) (2001), 171-182.
• [9] J. Dugundji, Topology, Allyn and Bacom, Boston, 1966.
• [10] R. Engelking, General Topology, PWN, Warszawa, 1977.
• [11] J.G. Hocking and G.S. Young, Topology, Addison-Wesley Publishing Company, Inc., Massachusetts, 1961.
• [12] W. Kryszewski, Homotopy properties of set-valued mappings, The Nicholas Copernicus University, Toruń, 1997.
• [13] W. Kryszewski, Graph-approximation of set-valued maps. A survey, Non. Anal. 2 (1998), 223-235.
• [14] W. Kryszewski, Graph-approximation of set-valued maps on noncompact domains, Topology & Appl. 83 (1988), 1-21.
• [15] E. Michael, Continuous selections I, Ann. of Math. 63 (2) (1956), 361-382.
• [16] D. Repovs and P.Semenov, On relative approximation theorems, Houston J. Math. 28 (2002), 497-509.
• [17] J. Schwartz, Non-linear Functional Analysis, Gordon and Breach, New York, 1966.
• [18] X. Zheng, Aproximate Selection Theorems and Their Applications, J. Math. Anal. Appl. 212 (1997), 88-97.

Identyfikatory

DOI

10.7151/dmdico.1085