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2001 | 144 | 2 | 135-152
Tytu艂 artyku艂u

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

Tre艣膰 / Zawarto艣膰
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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 蟽-finite measure 渭 is nonatomic, 1 鈮 p < 鈭, $L_{p}(T,E)$ is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x) 鈭 G(x) 鈮 鈭 for all x 鈭 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. 艁ojasiewicz, Jr. (1982), generalized by A. Fryszkowski (1983), A. Bressan and G. Colombo (1988)) which is simultaneously an 蔚-approximate continuous selector for F (as in the theorem of A. Cellina, G. Colombo and A. Fonda (1986), A. Bressan and G. Colombo (1988)).
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  • Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland
  • Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland
  • Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland
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bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-2-3
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