Generalized vector F-variational inequalities and vector F-complementarity problems for point-to-set mappings

Authors:
Nan-Jing Huang;Jun Li;H. B. Thompson
Affiliations:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China;Department of Mathematics, China West Normal University, Nanchong, Sichuan 637002, PR China;Department of Mathematics, The University of Queensland, Brisbane, Qld 4072, Australia
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

Citing 3
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Abstract

In this paper, we study a new generalized vector F-variational inequality and a new generalized vector F-complementarity problem for point-to-set mappings in Hausdorff topological vector spaces. We establish the equivalence between the generalized vector F-variational inequality and the generalized vector F-complementarity problem under certain assumptions. By considering the existence of solutions for the vector F-variational inequality with a single-valued mapping and using the continuous selection theorem, we obtain some new existence theorems of solutions for the generalized vector F-variational inequality and the generalized vector F-complementarity problem, respectively.