Hölder Continuity of the Solution Set of the Ky Fan Inequality (original) (raw)

Access this article

Log in via an institution

Subscribe and save

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

1. Fan, K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequality III, pp. 103–113. Academic Press, New York (1972)
   Google Scholar
2. Brézis, H., Nirenberg, L., Stampacchia, G.: A remark on Ky Fan’s minimax principle. Boll. Unione Mat. Ital. VI(III), 129–132 (1972)
   Google Scholar
3. Ansari, Q.H., Yao, J.C.: An existence result for the generalized vector equilibrium problem. Appl. Math. Lett. 12, 53–56 (1999)
   Article MathSciNet MATH Google Scholar
4. Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123–145 (1994)
   MathSciNet MATH Google Scholar
5. Giannessi, F.: Vector Variational Inequalities and Vector Equilibria: Mathematical Theories. Kluwer Academic, Dordrecht (2000)
   Book Google Scholar
6. Li, X.B., Li, S.J.: Existences of solutions for generalized vector quasiequilibrium problems. Optim. Lett. 4, 17–28 (2010)
   Article MathSciNet MATH Google Scholar
7. Anh, L.Q., Khanh, P.Q.: Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems. J. Math. Anal. Appl. 294, 699–711 (2004)
   Article MathSciNet MATH Google Scholar
8. Bianchi, M., Pini, R.: A note on stability for parametric equilibrium problems. Oper. Res. Lett. 31, 445–450 (2003)
   Article MathSciNet MATH Google Scholar
9. Bianchi, M., Pini, R.: Sensitivity for parametric vector equilibria. Optimization 55, 221–230 (2006)
   Article MathSciNet MATH Google Scholar
10. Chen, C.R., Li, S.J., Teo, K.L.: Solution semicontinuity of parametric generalized vector equilibrium problems. J. Glob. Optim. 45, 309–318 (2009)
    Article MathSciNet MATH Google Scholar
11. Li, X.B., Li, S.J.: Continuity of approximate solution mappings for parametric equilibrium problems. J. Glob. Optim. 51, 541–548 (2011)
    Article MATH Google Scholar
12. Yen, N.D.: Hölder continuity of solutions to parametric variational inequalities. Appl. Math. Optim. 31, 245–255 (1995)
    Article MathSciNet MATH Google Scholar
13. Mansour, M.A., Riahi, H.: Sensitivity analysis for abstract equilibrium problems. J. Math. Anal. Appl. 306, 684–691 (2005)
    Article MathSciNet MATH Google Scholar
14. Anh, L.Q., Khanh, P.Q.: On the Hölder continuity of solutions to multivalued vector equilibrium problems. J. Math. Anal. Appl. 321, 308–315 (2006)
    Article MathSciNet MATH Google Scholar
15. Anh, L.Q., Khanh, P.Q.: Uniqueness and Hölder continuity of solution to multivalued vector equilibrium problems in metric spaces. J. Glob. Optim. 37, 449–465 (2007)
    Article MathSciNet MATH Google Scholar
16. Anh, L.Q., Khanh, P.Q.: Sensitivity analysis for multivalued quasiequilibrium problems in metric spaces: Hölder continuity of solutions. J. Glob. Optim. 42, 515–531 (2008)
    Article MathSciNet MATH Google Scholar
17. Anh, L.Q., Khanh, P.Q.: Hölder continuity of the unique solution to quasiequilibrium problems in metric spaces. J. Optim. Theory Appl. 141, 37–54 (2009)
    Article MathSciNet MATH Google Scholar
18. Li, S.J., Li, X.B., Wang, L.N., Teo, K.L.: The Hölder continuity of solutions to generalized vector equilibrium problems. Eur. J. Oper. Res. 199, 334–338 (2009)
    Article MATH Google Scholar
19. Li, S.J., Chen, C.R., Li, X.B., Teo, K.L.: Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems. Eur. J. Oper. Res. 210, 148–157 (2011)
    Article MathSciNet MATH Google Scholar
20. Li, S.J., Li, X.B.: Hölder continuity of solutions to parametric weak generalized Ky Fan inequality. J. Optim. Theory Appl. 149, 540–553 (2011)
    Article MathSciNet MATH Google Scholar
21. Lee, G.M., Kim, D.S., Lee, B.S., Yen, N.D.: Vector variational inequality as a tool for studying vector optimization problems. Nonlinear Anal. 34, 745–765 (1998)
    Article MathSciNet MATH Google Scholar
22. Mansour, M.A., Ausssel, D.: Quasimonotone variational inequalities and quasiconvex programming: quantitative stability. Pac. J. Optim. 2, 611–626 (2006)
    MathSciNet MATH Google Scholar

Download references