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  • Research Article
  • Open Access

Parametric problem of completely generalized quasi-variational inequalities

Journal of Inequalities and Applications20062006:86869

  • Received: 29 August 2004
  • Accepted: 29 June 2005
  • Published:


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.


  • Sensitivity Analysis
  • Parametric Problem


Authors’ Affiliations

Department of Mathematics, Aligarh Muslim University, Aligarh, (UP), 202002, India
Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, P.O. Box 1745, Dhahran, 31261, Saudi Arabia


  1. Ahmad R, Kazmi KR, Salahuddin : Completely generalized non-linear variational inclusions involving relaxed Lipschitz and relaxed monotone mappings. Nonlinear Analysis Forum 2000, 5: 61–69.MATHMathSciNetGoogle Scholar
  2. Cottle RW, Giannessi F, Lions JL: Variational Inequalities and Complementarity Problems, Theory and Applications. John Wiley & Sons, Chichester; 1980:xvii+408.MATHGoogle Scholar
  3. Dafermos S: Sensitivity analysis in variational inequalities. Mathematics of Operations Research 1988,13(3):421–434. 10.1287/moor.13.3.421MATHMathSciNetView ArticleGoogle Scholar
  4. Ding XP, Luo CL: On parametric generalized quasi-variational inequalities. Journal of Optimization Theory and Applications 1999,100(1):195–205. 10.1023/A:1021777217261MATHMathSciNetView ArticleGoogle Scholar
  5. Kinderlehrer D, Stampacchia G: An Introduction to Variational Inequalities and Their Applications, Pure and Applied Mathematics. Volume 88. Academic Press, New York; 1980:xiv+313.MATHGoogle Scholar
  6. Lim T-C: On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. Journal of Mathematical Analysis and Applications 1985,110(2):436–441. 10.1016/0022-247X(85)90306-3MATHMathSciNetView ArticleGoogle Scholar
  7. Mukherjee RN, Verma HL: Sensitivity analysis of generalized variational inequalities. Journal of Mathematical Analysis and Applications 1992,167(2):299–304. 10.1016/0022-247X(92)90207-TMATHMathSciNetView ArticleGoogle Scholar
  8. Nadler SB Jr.: Multi-valued contraction mappings. Pacific Journal of Mathematics 1969,30(2):475–488.MATHMathSciNetView ArticleGoogle Scholar
  9. Noor MA: An iterative scheme for a class of quasivariational inequalities. Journal of Mathematical Analysis and Applications 1985,110(2):463–468. 10.1016/0022-247X(85)90308-7MATHMathSciNetView ArticleGoogle Scholar
  10. Robinson SM: Sensitivity analysis of variational inequalities by normal-map techniques. In Variational Inequalities and Network Equilibrium Problems (Erice, 1994). Edited by: Giannessi F, Maugeri A. Plenum, New York; 1995:257–269.View ArticleGoogle Scholar
  11. Salahuddin : Some aspects of variational inequalities, M.S. thesis. AMU, Aligarh; 2000.Google Scholar
  12. Salahuddin : On parametric generalized quasivariational inequalities with related Lipschitz and relaxed monotone mappings. Advances in Nonlinear Variational Inequalities 2002,5(1):107–114.MATHMathSciNetGoogle Scholar
  13. Siddiqi AH, Ansari QH: An algorithm for a class of quasivariational inequalities. Journal of Mathematical Analysis and Applications 1990,145(2):413–418. 10.1016/0022-247X(90)90409-9MATHMathSciNetView ArticleGoogle Scholar
  14. Yen ND: Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraint. Mathematics of Operations Research 1995,20(3):695–708. 10.1287/moor.20.3.695MATHMathSciNetView ArticleGoogle Scholar