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Generalized Vector Quasivariational Inclusion Problems with Moving Cones
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Generalized Vector Quasivariational Inclusion Problems with Moving Cones
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Generalized Vector Quasivariational Inclusion Problems with Moving Cones
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Generalized Vector Quasivariational Inclusion Problems with Moving Cones
Generalized Vector Quasivariational Inclusion Problems with Moving Cones
Journal Article

Generalized Vector Quasivariational Inclusion Problems with Moving Cones

2010
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Overview
This paper deals with the generalized vector quasivariational inclusion Problem (P 1 ) (resp. Problem (P 2 )) of finding a point ( z 0 , x 0 ) of a set E × K such that ( z 0 , x 0 )∈ B ( z 0 , x 0 )× A ( z 0 , x 0 ) and, for all η ∈ A ( z 0 , x 0 ), where A : E × K →2 K , B : E × K →2 E , C : E × K →2 Y , F , G : E × K × K →2 Y are some set-valued maps and Y is a topological vector space. The nonemptiness and compactness of the solution sets of Problems (P 1 ) and (P 2 ) are established under the verifiable assumption that the graph of the moving cone C is closed and that the set-valued maps F and G are C -semicontinuous in a new sense (weaker than the usual sense of semicontinuity).