Skip to main content

Some Characteristic Quantities Associated with Homogeneous-Type and-Type Functions


Several characteristic quantities associated with homogeneous-type and-type functions are introduced and studied in this paper. Further, the concepts of-property and-property for a couple of functions are introduced and some quantities for a pair of homogeneous functions having-property and-property are obtained, respectively. As an application, a bound for the solution of the homogeneous complementarity problem with a-type function is derived.



  1. Fiedler M, Pták V: On matrices with non-positive off-diagonal elements and positive principal minors. Czechoslovak Mathematical Journal 1962, 12(87): 382–400.

    Google Scholar 

  2. Cottle RW, Pang J-S, Stone RE: The Linear Complementarity Problem, Computer Science and Scientific Computing. Academic Press, Boston, Mass, USA; 1992:xxiv+762.

    Google Scholar 

  3. Isac G: Complementarity Problems, Lecture Notes in Mathematics. Volume 1528. Springer, Berlin, Germany; 1992:vi+297.

    Google Scholar 

  4. Isac G: Topological Methods in Complementarity Theory, Nonconvex Optimization and Its Applications. Volume 41. Kluwer Academic Publishers, Dordrecht, The Netherlands; 2000:xiv+683.

    Google Scholar 

  5. Mathias R, Pang J-S: Error bounds for the linear complementarity problem with a -matrix. Linear Algebra and Its Applications 1990, 132: 123–136. 10.1016/0024-3795(90)90058-K

    Article  MathSciNet  MATH  Google Scholar 

  6. Xiu N, Zhang J: A characteristic quantity of -matrices. Applied Mathematics Letters 2002,15(1):41–46. 10.1016/S0893-9659(01)00090-8

    Article  MathSciNet  MATH  Google Scholar 

  7. Gowda MS: On the extended linear complementarity problem. Mathematical Programming 1996,72(1):33–50. 10.1007/BF02592330

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Ya-Ping Fang.

Rights and permissions

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

Reprints and permissions

About this article

Cite this article

Fang, YP., Huang, NJ. & Cho, Y.J. Some Characteristic Quantities Associated with Homogeneous-Type and-Type Functions. J Inequal Appl 2007, 084146 (2007).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: