CM-Selectors for pairs of oppositely semicontinuous multivalued maps with $𝕃_{p}$-decomposable values

• Autorzy: Hôǹg Thái Nguyêñ , Maciej Juniewicz , Jolanta Ziemińska
• Języki publikacji: EN

Abstrakty

EN

We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex $L_{p}(T,E)$-decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, $L_{p}(T,E)$ is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x) ∩ G(x) ≠ ∅ for all x ∈ X, then there exists a CM-selector for the pair (F,G), i.e. a continuous selector for G (as in the theorem of H. Antosiewicz and A. Cellina (1975), A. Bressan (1980), S. Łojasiewicz, Jr. (1982), generalized by A. Fryszkowski (1983), A. Bressan and G. Colombo (1988)) which is simultaneously an ε-approximate continuous selector for F (as in the theorem of A. Cellina, G. Colombo and A. Fonda (1986), A. Bressan and G. Colombo (1988)).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 144
• Numer: 2
• Strony: 135-152

Daty

wydano

2001

Twórcy

autor

Hôǹg Thái Nguyêñ

• Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland

autor

Maciej Juniewicz

• Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland

autor

Jolanta Ziemińska

• Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland

Identyfikatory

DOI

10.4064/sm144-2-3