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Generalized Vector Quasivariational Inclusion Problems with Moving Cones

Author

Listed:
  • P. H. Sach

    (Institute of Mathematics)

  • L. J. Lin

    (National Changhua University of Education)

  • L. A. Tuan

    (Ninh Thuan College of Pedagogy)

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).

Suggested Citation

  • P. H. Sach & L. J. Lin & L. A. Tuan, 2010. "Generalized Vector Quasivariational Inclusion Problems with Moving Cones," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 607-620, December.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:3:d:10.1007_s10957-010-9670-9
    DOI: 10.1007/s10957-010-9670-9
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    References listed on IDEAS

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    1. N. X. Hai & P. Q. Khanh, 2007. "Systems of Set-Valued Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 55-67, October.
    2. L.J. Lin & Q.H. Ansari & J.Y. Wu, 2003. "Geometric Properties and Coincidence Theorems with Applications to Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 121-137, April.
    3. D. T. Luc, 2008. "An Abstract Problem in Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 65-76, July.
    4. X. P. Ding & J. Y. Park, 2004. "Generalized Vector Equilibrium Problems in Generalized Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 327-353, February.
    5. L. J. Lin & W. P. Wan, 2004. "KKM Type Theorems and Coincidence Theorems with Applications to the Existence of Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 105-122, October.
    6. N. X. Tan, 2004. "On the Existence of Solutions of Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 619-638, December.
    7. S. Li & K. Teo & X. Yang, 2005. "Generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 385-397, July.
    8. J. Y. Fu & S. H. Wang & Z. D. Huang, 2007. "New Type of Generalized Vector Quasiequilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 643-652, December.
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    Cited by:

    1. Ali Farajzadeh & Byung Soo Lee & Somyot Plubteing, 2016. "On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 584-599, February.
    2. Anulekha Dhara & Dinh Luc, 2014. "A solution method for linear variational relation problems," Journal of Global Optimization, Springer, vol. 59(4), pages 729-756, August.
    3. Pham Sach & Nguyen Minh, 2013. "Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities," Journal of Global Optimization, Springer, vol. 57(4), pages 1401-1418, December.
    4. Le Tuan & Gue Lee & Pham Sach, 2010. "Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones," Journal of Global Optimization, Springer, vol. 47(4), pages 639-660, August.

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