Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: PARAMETRIC PROBLEM OF COMPLETELY GENERALIZED QUASI-VARIATIONAL INEQUALITIES | PARAMETRIC PROBLEM OF COMPLETELY GENERALIZED QUASI-VARIATIONAL INEQUALITIES SALAHUDDIN M. K. AHMAD AND A. H. SIDDIQI Received 29 August 2004 Revised 27 January 2005 Accepted 29 June 2005 This paper is devoted to the study of behaviour and sensitivity analysis of the solution for a class of parametric problem of completely generalized quasi-variational inequalities. Copyright 2006 Salahuddin et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Sensitivity analysis of solutions for variational inequalities with single-valued mappings has been studied by many authors with different techniques in finite dimensional spaces and Hilbert spaces 3 4 7 11 14 . Robinson 10 has dealt with the sensitivity analysis of solutions for the classical variational inequalities over polyhedral convex sets in finite dimensional spaces. In this paper we study the behaviour and sensitivity analysis of solutions for a class of parametric problem of completely generalized quasi-variational inequalities with setvalued mappings without the differentiability assumptions. 2. Preliminaries Let H be a real Hilbert space with x 2 x x 2H the family of all nonempty bounded subsets of H and C H the family of all nonempty compact subsets of H. Let 8 2H 0 00 be defined by 8 A B sup a - fib a G A b G B VA B G 2H and let H C H 0 00 be defined by H A B ma supd x B supd A y i VA B G C H xgA yGB Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID 86869 Pages 1-12 DOI JIA 2006 86869 2 Parametric problem of quasi-variational inequalities where d x B inf x- y . yeB Then 2H 8 and C H H are complete metric spaces H is the Hausdorff metric on C H . We now consider the parametric problem of completely generalized quasi-variational inequalities. Let Q be a nonempty open subset
