MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITY WITH LOCAL NON-POSITIVITY

- Journal title : Communications of the Korean Mathematical Society
- Volume 24, Issue 3, 2009, pp.425-432
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2009.24.3.425

Title & Authors

MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITY WITH LOCAL NON-POSITIVITY

Lee, Byung-Soo;

Lee, Byung-Soo;

Abstract

This paper introduces a local non-positivity of two set-valued mappings (F,Q) and considers the existences and properties of solutions for set-valued mixed vector FQ-implicit variational inequality problems and set-valued mixed vector FQ-complementarity problems in the neighborhood of a point belonging to an underlined domain K of the set-valued mappings, where the neighborhood is contained in K. This paper generalizes and extends many results in [1, 3-7].

Keywords

mixed vector FQ-implicit complementarity problem;mixed vector FQ-implicit variational inequality problem;positively homogeneous mapping;convex cone;upper semicontinuity;lower semicontinuity;locally non-positive;

Language

English

References

1.

Y. P. Fang and N. J. Huang, The vector F-complementarity problem with demipseudomonotone mappings in Banach spaces, Appl. Math. Lett. 16 (2003), 1019–1024

3.

N. J. Huang and J. Li, F-implicit complementarity problems in Banach spaces, Z. Anal. Anwendungen 23 (2004), 293–302

4.

B. S. Lee, Mixed vector FQ-implicit variational inequalities with FQ-complementatity problems, submitted

5.

B. S. Lee, M. F. Khan, and Salahuddin, Vector F-implicit complementarity problems with corresponding variational inequality problems, Appl. Math. Lett. 20 (2007), 433–438

6.

J. Li and N. J. Huang, Vector F-implicit complementarity problems in Banach spaces, Appl. Math. Lett. 19 (2006), 464–471

7.

H. Y. Yin, C. X. Xu, and Z. X. Zhang, The F-complementarity problems and its equivalence with the least element problem, Acta Math. Sinica 44 (2001), 679–686