A selection theorem of Helly type and its applications

• Autorzy: Ehrhard Behrends , Kazimierz Nikodem
• Języki publikacji: EN

Abstrakty

EN

We prove an abstract selection theorem for set-valued mappings with compact convex values in a normed space. Some special cases of this result as well as its applications to separation theory and Hyers-Ulam stability of affine functions are also given.

Kategorie tematyczne

• 26B25: Convexity, generalizations
• 52A35: Helly-type theorems and geometric transversal theory
• 39B72: Systems of functional equations and inequalities
• 54C65: Selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 116
• Numer: 1
• Strony: 43-48

Daty

wydano

1995

otrzymano

1994-09-13

poprawiono

1995-03-01

Twórcy

autor

Ehrhard Behrends

• Freie Universität Berlin, I Mathematisches Institut, Arnimallee 3, 14195 Berlin, Germany

autor

Kazimierz Nikodem

• Department Of Mathematics, Łódź Technical University, Bielsko-Biała Branch, Willowa 2, 43-309 Bielsko-Biała, Poland

Bibliografia

• [1] K. Baron, J. Matkowski and K. Nikodem, A sandwich with convexity, Math. Pannonica 5 (1994), 139-144.
• [2] D. H. Hyers and S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc. 3 (1952), 821-828.
• [3] K. Nikodem and S. Wąsowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math., to appear.
• [4] F. A. Valentine, Convex Sets, McGraw-Hill, New York, 1964.
• [5] S. Wasowicz, On affine selections of set-valued functions, to appear.