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Parametric problem of completely generalized quasi-variational inequalities

Abstract

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.

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References

  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.

    MATH  MathSciNet  Google Scholar 

  2. Cottle RW, Giannessi F, Lions JL: Variational Inequalities and Complementarity Problems, Theory and Applications. John Wiley & Sons, Chichester; 1980:xvii+408.

    MATH  Google Scholar 

  3. Dafermos S: Sensitivity analysis in variational inequalities. Mathematics of Operations Research 1988,13(3):421–434. 10.1287/moor.13.3.421

    Article  MATH  MathSciNet  Google 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:1021777217261

    Article  MATH  MathSciNet  Google 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.

    MATH  Google 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)90306-3

    Article  MATH  MathSciNet  Google 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-T

    Article  MATH  MathSciNet  Google Scholar 

  8. Nadler SB Jr.: Multi-valued contraction mappings. Pacific Journal of Mathematics 1969,30(2):475–488.

    Article  MATH  MathSciNet  Google 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)90308-7

    Article  MATH  MathSciNet  Google 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.

    Chapter  Google 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.

    MATH  MathSciNet  Google 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)90409-9

    Article  MATH  MathSciNet  Google 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.20.3.695

    Article  MATH  MathSciNet  Google Scholar 

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Salahuddin, Ahmad, M.K. & Siddiqi, A.H. Parametric problem of completely generalized quasi-variational inequalities. J Inequal Appl 2006, 86869 (2006). https://doi.org/10.1155/JIA/2006/86869

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  • DOI: https://doi.org/10.1155/JIA/2006/86869

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