Results 201 to 210 of about 6,189,727 (240)

A Note on Quasiconvex Set-Valued Maps

OPSEARCH, 2003
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Lalitha, C. S., Davar, Sonia
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Convexity Criteria for Set-Valued Maps

Set-Valued Analysis, 1997
The paper gives necessary and sufficient conditions for a set-valued function \(F\) between Banach spaces \(X\) and \(Y\) to be convex with respect to a convex cone \(K\subset Y\), i.e., to satisfy \[ tF(x_1)+ (1-t)F(x_2)\subset\text{cl}(F(tx_1+ (1-t)x_2)),\quad x_1,x_2\in X,\quad t\in[0,1].
Pham Huu Sach, Nguyen Dong Yen
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Fuzzy integrals of set-valued mappings and fuzzy mappings

Fuzzy Sets and Systems, 1995
In this paper, the fuzzy integral is generalized to the case where the integrand can be a set-valued mapping or, even more, a fuzzy mapping. Fatou's lemma and Lebesgue's convergence theorem for sequences of such kind of fuzzy integrals are also discussed.
Deli Zhang, Caimei Guo
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Set-Valued Maps

2009
We shall gather in this chapter some of the results dealing with set-valued maps that we shall need. Only the properties of upper semicontinuous set-valued maps and, among them, the Convergence Theorem 2.4.4, and some notions on the set-valued analogues of continuous linear operators, the closed convex processes are required in the short term.
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Attempts to Approximate a Set-Valued Mapping

1985
Given a multi-valued mapping F, we address the problem of finding another multi-valued mapping H that agrees locally with F in some sense. We show that, contrary to the scalar case, introducing a derivative of F is hardly convenient. For the case when F is convex-compact-valued, we give some possible approximations, and at the same time we show their ...
Demyanov, V.F., Lemarechal, C., Zowe, J.
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Approximation of continuous set-valued maps by constant set-valued maps with image balls

Mathematical Notes, 2007
M. S. Nikolskii showed in 1990 that a continuous set-valued map with compact convex images was uniformly approximated in the Hausdorff metric by constant set-valued maps with convex images. In this paper the authors show that the problem of the best uniform approximation in the Hausdorff metric of a continuous set-valued map with finite-dimensional ...
Dudov, S. I., Konoplev, A. B.
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Weak and Strong Subgradients of Set-Valued Maps

Journal of Optimization Theory and Applications, 2011
The authors consider set-valued optimization problems and introduce a new so-called strong subgradient of a set-valued map. Then, they compare this new concept with the well-known weak subgradient and provide sufficient conditions for the existence of these both types of subgradients. Finally, several optimality conditions are discussed.
Elvira Hernández, Luis Rodríguez-Marín   +1 more
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Cosmically Lipschitz Set-Valued Mappings

Set-Valued Analysis, 2002
In view of applications to necessary optimality conditions in optimal control, to the theory of Hamilton-Jacobi equations and to invariant sets for differential inclusions, the author proves a large number of results (some 9 theorems, 6 propositions and 8 lemmas) concerning, mainly, the so-called ``cosmic Lipschitzianity'' of set-valued mappings ...
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On pseudomonotone set-valued mappings

Nonlinear Analysis: Theory, Methods & Applications, 2008
A common generalization of the algebraic and topological pseudomonotonicity for set-valued mappings in topological vector spaces is introduced. Existence results for variational inequalities governed by such maps are given.
Inoan, D., Kolumbán, J.
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Approximation of nonconvex set valued mappings

1985
The authors give a proof for the following theorem, which is a result on the approximation of a nonconvex set-valued mapping by a continuous function. Suppose that \(V\subset I\times R^ n\) and that F:V\(\to (non\)- empty compact contractible subsets of \(R^ n\}\) is an upper semicontinuous multiple valued function.
ANICHINI, GIUSEPPE, CONTI, GIUSEPPE, ZECCA, PIETRO   +2 more
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