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

Hôǹg Thái Nguyêñ; Maciej Juniewicz; Jolanta Ziemińska

Studia Mathematica (2001)

- Volume: 144, Issue: 2, page 135-152
- ISSN: 0039-3223

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topHôǹg Thái Nguyêñ, Maciej Juniewicz, and Jolanta Ziemińska. "CM-Selectors for pairs of oppositely semicontinuous multivalued maps with $_{p}$-decomposable values." Studia Mathematica 144.2 (2001): 135-152. <http://eudml.org/doc/286279>.

@article{HôǹgTháiNguyêñ2001,

abstract = {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)).},

author = {Hôǹg Thái Nguyêñ, Maciej Juniewicz, Jolanta Ziemińska},

journal = {Studia Mathematica},

keywords = {decomposable set; combinative selector; -approximate continuous selector; semicontinuous multivalued map; non-convex decomposable value; semicontinuous multifunction; lower semicontinuity; -upper semicontinuity; multivalued map satisfying one-sided estimates},

language = {eng},

number = {2},

pages = {135-152},

title = {CM-Selectors for pairs of oppositely semicontinuous multivalued maps with $_\{p\}$-decomposable values},

url = {http://eudml.org/doc/286279},

volume = {144},

year = {2001},

}

TY - JOUR

AU - Hôǹg Thái Nguyêñ

AU - Maciej Juniewicz

AU - Jolanta Ziemińska

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

JO - Studia Mathematica

PY - 2001

VL - 144

IS - 2

SP - 135

EP - 152

AB - 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)).

LA - eng

KW - decomposable set; combinative selector; -approximate continuous selector; semicontinuous multivalued map; non-convex decomposable value; semicontinuous multifunction; lower semicontinuity; -upper semicontinuity; multivalued map satisfying one-sided estimates

UR - http://eudml.org/doc/286279

ER -

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