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2007 | 27 | 2 | 265-294
Tytuł artykułu

Continuous selections and approximations in α-convex metric spaces

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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.
Twórcy
autor
  • 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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1085
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