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Cerami (C) Condition and Mountain Pass Theorem for Multivalued Mappings

, 2002
Alexandru Kristály, Cs. Varga
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Theorems on Inclusion for Multivalued Mappings

Ukrainian Mathematical Journal, 2014
Let \(X,Y\) be Banach spaces and \(F:A\rightrightarrows Y\) a set-valued mapping. A restriction of \(F\) to a subset \(B\) of \(A\) is a set-valued mapping \(F_1: B\rightrightarrows Y\) such that \(F_1(x)\subset F(x)\) for all \(x\in B\) and \(F_1(x)=\emptyset\) for all \(x\in A\setminus B\). One says that \(F\) satisfies the coacute angle condition if,
Zelinskii, Yu. B., Klishchuk, B. A., Tkachuk, M. V.   +2 more
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Equivariant multivalues maps

Russian Mathematical Surveys, 1994
The author presents an interesting generalization of the Borsuk antipodal theorem from the case of single-valued equivariant mappings to the case of multivalued equivariant mappings.
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On the Projections of Multivalued Maps

Journal of Optimization Theory and Applications, 1997
The problem considered in the paper can be described very roughly as follows. There are given an open set \(\Omega\subset{\mathbb{R}}^n,\) an integer \(m,\) a multivalued map \(\Pi:\Omega\rightarrow 2^{{\mathbb{R}}^{m\times n}}\) and the set \(\Pi'\) of square integrable selections of \(\Pi.\) The author gives sufficient conditions for inclusions of ...
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Multivalued Analysis and Differential Properties of Multivalued Mappings

Journal of Mathematical Sciences, 2003
Let \(X\) and \(Y\) be finite-dimensional spaces; \(F: X \rightarrow 2^Y\) a multimap and \(f: X \times Y \rightarrow \mathbb{R}\) a function. The functions \(\varphi, \Phi : X \rightarrow \mathbb{R} \cup \{\pm \infty\},\) \[ \varphi (x) = \inf \{f(x,y) | y \in F(x)\}, \] \[ \Phi (x) = \sup \{f(x,y) | y \in F(x)\} \] are said to be marginal functions ...
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Differentiation of Multivalued Mappings. T-Derivative

Ukrainian Mathematical Journal, 2000
Summary: We consider several approaches to differentiation of multivalued mappings and introduce a new definition of derivative (\(T\)-derivative) which generalizes the Hukuhara derivative.
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A class of multivalued mappings

Siberian Mathematical Journal, 1985
Let \(X_ p\) be the closed unit ball of a p-dimensional Euclidean space \(E_ p\), \(\Pi_ p\) be the set of all nonvoid closed subsets of \(X_ p\) and finally \(\Omega_ p\) be the family of all linear selfadjoint operators \(A: E_ p\to E_ p\) of the norm at most 1.
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Lower Semicontinuity of Multivalued Linearization Mappings

SIAM Journal on Control, 1973
Many results in mathematical programming require lower semicontinuity of the multi-valued function obtained from a constraint set by replacing the functions defining the set by their linearizations about a point. In this paper we give a simple sufficient condition, involving the gradients of the active linearized constraints, for this property to hold.
Robinson, Stephen M., Meyer, Robert R.
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