Skip to main content
  • Research Article
  • Open access
  • Published:

On almost coincidence points in generalized convex spaces

Abstract

We prove an almost coincidence point theorem in generalized convex spaces. As an application, we derive a result on the existence of a maximal element and an almost coincidence point theorem in hyperconvex spaces. The results of this paper generalize some known results in the literature.

[12345678910111213]

References

  1. Border KC: Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press, Cambridge; 1985:viii+129.

    Book  MATH  Google Scholar 

  2. Espínola R, Khamsi MA: Introduction to Hyperconvex Spaces. Kluwer Academic, Dordrecht; 2001.

    Book  MATH  Google Scholar 

  3. Khamsi MA: KKM and Ky Fan theorems in hyperconvex metric spaces. Journal of Mathematical Analysis and Applications 1996,204(1):298–306. 10.1006/jmaa.1996.0438

    Article  MathSciNet  MATH  Google Scholar 

  4. Kim I-S, Park S: Almost fixed point theorems of the Fort type. Indian Journal of Pure and Applied Mathematics 2003,34(5):765–771.

    MathSciNet  MATH  Google Scholar 

  5. Kirk WA, Shin SS: Fixed point theorems in hyperconvex spaces. Houston Journal of Mathematics 1997,23(1):175–188.

    MathSciNet  MATH  Google Scholar 

  6. Lin L-J: Applications of a fixed point theorem in -convex space. Nonlinear Analysis 2001,46(5):601–608. 10.1016/S0362-546X(99)00456-3

    Article  MathSciNet  MATH  Google Scholar 

  7. Nikodem K: K-Convex and K-Concave Set-Valued Functions. Politechnika, Lodzka; 1989.

    Google Scholar 

  8. Park S: Continuous selection theorems in generalized convex spaces. Numerical Functional Analysis and Optimization 1999,20(5–6):567–583. 10.1080/01630569908816911

    Article  MathSciNet  MATH  Google Scholar 

  9. Park S: Remarks on fixed point theorems for new classes of multimaps. Journal of the Academy of Natural Sciences, Republic of Korea 2004, 43: 1–20.

    Google Scholar 

  10. Park S, Kim H: Admissible classes of multifunction on generalized convex spaces. Proceedings of College Nature Science, Seoul National University 1993, 18: 1–21.

    Google Scholar 

  11. Park S, Kim H: Coincidence theorems for admissible multifunctions on generalized convex spaces. Journal of Mathematical Analysis and Applications 1996,197(1):173–187. 10.1006/jmaa.1996.0014

    Article  MathSciNet  MATH  Google Scholar 

  12. Park S, Kim H: Foundations of the KKM theory on generalized convex spaces. Journal of Mathematical Analysis and Applications 1997,209(2):551–571. 10.1006/jmaa.1997.5388

    Article  MathSciNet  MATH  Google Scholar 

  13. Yuan GX-Z: KKM Theory and Applications in Nonlinear Analysis, Monographs and Textbooks in Pure and Applied Mathematics. Volume 218. Marcel Dekker, New York; 1999:xiv+621.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zoran D Mitrović.

Rights and permissions

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.

Reprints and permissions

About this article

Cite this article

Mitrović, Z.D. On almost coincidence points in generalized convex spaces. Fixed Point Theory Appl 2006, 91397 (2006). https://doi.org/10.1155/FPTA/2006/91397

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/FPTA/2006/91397

Keywords