Open Access Research

Continuity of solutions for parametric generalized quasi-variational relation problems

Nguyen Van Hung

Author Affiliations

Department of Mathematics, Dong Thap University, 783 Pham Huu Lau Street, Ward 6, Cao Lanh City, Vietnam

Fixed Point Theory and Applications 2012, 2012:102 doi:10.1186/1687-1812-2012-102

Published: 21 June 2012

Abstract

In this article, we establish sufficient conditions for the solution sets of parametric generalized quasi-variational relation problems with the stability properties such as the upper semicontinuity, lower semi-continuity, the Hausdorff lower semicontinuity, continuity, Hausdorff continuity, and closedness. Our results improve recent existing ones in the literature.

Mathematics Subject Classification 2010: 90C31; 49J53; 49J40; 49J45.

Keywords:
quasi-variational relation problems; upper semicontinuity; lower semicontinuity; Hausdorff lower semicontinuity; upper semicontinuity; continuity; H-continuity; closedness