Results 241 to 250 of about 608,522 (264)

Set-valued mappings

1998
Here we deal with some properties of set-valued mappings. These properties will be applied in our further considerations. The notion of a setvalued mapping is a generalization (in a certain sense) of the notion of an ordinary mapping. First, let us recall that a set-valued mapping (or a multi-valued mapping, or a multi-valued function) is a mapping of ...
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Set-Valued Maps

2008
In robust control theory, an uncertain dynamical system is described by a set of models rather than a single model. For example, a system with an unknown parameter generates a set of models, one for each possible value of the parameter; likewise for a system with an unknown disturbance (which can be a function of time as well as state variables and ...
Randy A. Freeman, Petar Kokotović
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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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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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Weak Subdifferentials for Set-Valued Mappings

Journal of Optimization Theory and Applications, 2013
The authors investigate the weak subdifferential for set-valued mappings, which was originally introduced by \textit{G. Y. Chen} and \textit{J. Jahn} [Math. Methods Oper. Res. 48, No. 2, 187--200 (1998; Zbl 0927.90095)]. After giving some preliminaries in Section 2, two existence theorems of weak subgradients for set-valued mappings are proven in ...
Long, X. J., Peng, J. W., Li, X. B.
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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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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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Set-Valued Mappings Redux

2013
Let \( X \) and \( Y \) be two finite sets with \( \left| {\, X{\,}} \right|=m \) and \( \left| {\,Y{\,}} \right|=n ...
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Congeries Set-Valued Mappings

2017
Part I of RL is a pentateuchal exploration of the algebraic theory of set-valued mappings. It also contains the motivations and other natural philosophical reasons on why I consider them congenial and congenital morphisms for relational biology.
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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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