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Equivalents of an approximate variational principle for vector-valued functions and applications

Author

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  • G. Y. Chen
  • X. X. Huang
  • G. M. Lee

Abstract

In [1], we gave a unified variational principle for vector valued functions. In this paper, we give four equivalents of a corollary of this principle, generalizing the equivalence results of [3] to the vector case and improving the equivalence results of [5]. We also applied one of the equivalents to derive the vector form of the “Drop Theorem” ([3]). Applying the unified variational principle, we obtained a fixed point theorem for directional contractions as an application of our vector variational principle, generalizing a fixed point theorem for directional contractions in [9]. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • G. Y. Chen & X. X. Huang & G. M. Lee, 1999. "Equivalents of an approximate variational principle for vector-valued functions and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 125-136, March.
    • Handle: RePEc:spr:mathme:v:49:y:1999:i:1:p:125-136
    DOI: 10.1007/s001860050017
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    Cited by:

    1. Behnam Soleimani, 2014. "Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 605-632, August.

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