Optimization Letters

, Volume 8, Issue 7, pp 2127–2134 | Cite as

When a vector quasimonotone mapping is a vector monotone mapping

Original Paper
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Abstract

In this paper we provide a sufficient conditions that under them a vector quasimonotone set-valued mapping transfer to a vector monotone set-valued mapping. In fact this note is a vector version of the papers (Farajzadeh, J Ineq Appl 2012:192, 2012) and (Hadjisavvas, Appl Math Lett 19:913–915, 2006).

Keywords

Monotone map Vector pseudomonotone map Vector quasimonotone map Surjective property 
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Notes

Acknowledgments

The authors are very thankful to the anonymous referee for valuable comments.

References

  1. 1.
    Chen, B., Chen, X., Kanzow, C.: A penalized Fischer-Burmeister NCP-function. Math. Program. Ser. A 88(1), 211–216 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Deimling, K.: Nonlinear functuinal analysis. Springer, Berlin (1988)Google Scholar
  3. 3.
    Farajzadeh, A.P., Karamian, A., Plubtieng, S.: On the translations of quasimonotone maps and monotonicity. J. Ineq. Appl. 2012, 192 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Jinghui, Q.: Characterization of solid cones. Acta Mathematica Scientia. 25B(2), 408–416 (2008)CrossRefGoogle Scholar
  5. 5.
    Hadjisavvas, N.: Translations of quasimonotone maps and monotonicity. Appl. Math. Lett. 19, 913–915 (2006)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    He, Y.: Asymptotic analysis and error bounds in optimization, Ph.D. Thesis. The Chinese University of Hong Kong (2001)Google Scholar
  7. 7.
    He, Y.: A relationship between pseudomonotone and monotone mappings. Appl. Math. Lett. 17, 459–461 (2004)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Isac, G., Motreanu, D.: Pseudomonotonicity and quasiomonotonicity by translations versus monotonicity in Hilbert spaces. Austral. J. Math. Anal. 1, 1–8 (2004)MathSciNetGoogle Scholar
  9. 9.
    Karamardian, S., Schaible, S.: Seven kinds of monotone maps. J. Optim. Theory Appl. 66, 37–46 (1990)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Karamardian, S., Schaible, S., Crouuzeix, J.P.: Characterizations of generalized monotone maps. J. Optim. Theory Appl. 76, 399–413 (1993)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Rockafellar, R.T., Wets, R.J.B.: Variational analysis. Springer, Berlin (1998)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsRazi UniversityKermanshahIran
  2. 2.Department of Mathematics, Faculty of ScienceNaresuan UniversityPhitsanulokThailand

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