Calculus of Set Valued Functions and Control
نویسندگان
چکیده
منابع مشابه
Monotone set-valued functions defined by set-valued Choquet integrals
In this paper, some properties of the monotone set-valued function defined by the set-valued Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as null-additivity, strong order continuity, property(S) and pseudometric generating property, etc., are preserved by the new set-valued function. It is also shown that integr...
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The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gâteaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key elem...
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We investigate analyticity of joint spectra of Am-valued holomorphic mappings, where A denotes a complex Banach algebra. We show also that if K is an analytic set-valued function whose values are compact subsets of Cn and d is the transfinite diameter in Cn, then the upper-semicontinuous regularization of logd(X) is plurisubharmonic. Moreover, we give higher dimensional extensions of Aupetit's ...
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Let Σ : M → 2 \ {∅} be a set-valued function defined on a Hausdorff compact topological space M and taking values in the normed space (Y, ‖·‖). We deal with the problem of finding the best Chebyshev type approximation of the set-valued function Σ by a singlevalued function g from a given closed convex set V ⊂ C(M, Y ). In an abstract setting this problem is posed as the extremal problem supt∈M ...
متن کاملPseudo-integral of Set-valued Functions
An approach to the integration of set-valued functions based on the pseudo-integral has been proposed. Some basic properties of the pseudo-integral of set-valued functions have been shown.
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 1968
ISSN: 0022-2518
DOI: 10.1512/iumj.1969.18.18006