Generalized Vector Quasivariational Inclusion Problems with Moving Cones

P. H. Sach, L. J. Lin () and L. A. Tuan
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P. H. Sach: Institute of Mathematics
L. J. Lin: National Changhua University of Education
L. A. Tuan: Ninh Thuan College of Pedagogy

Journal of Optimization Theory and Applications, 2010, vol. 147, issue 3, No 13, 607-620

Abstract: Abstract This paper deals with the generalized vector quasivariational inclusion Problem (P1) (resp. Problem (P2)) 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), $$\begin{array}{l}F(z_0,x_0,\eta)\subset G(z_0,x_0,x_0)+C(z_0,x_0)\cr \mathrm{[resp.}F(z_0,x_0,x_0)\subset G(z_0,x_0,\eta)+C(z_0,x_0)],\end{array}$$ 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 (P1) and (P2) 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).

Keywords: Generalized vector quasivariational inclusion problem; Set-valued maps; Existence theorems; Moving cones; Generalized concavity (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-010-9670-9

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