Open Access

On almost coincidence points in generalized convex spaces

Fixed Point Theory and Applications20062006:91397

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

Received: 19 April 2006

Accepted: 7 June 2006

Published: 1 October 2006

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]

Authors’ Affiliations

(1)
Faculty of Electrical Engineering, University of Banja Luka

References

  1. Border KC: Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press, Cambridge; 1985:viii+129.View ArticleMATHGoogle Scholar
  2. Espínola R, Khamsi MA: Introduction to Hyperconvex Spaces. Kluwer Academic, Dordrecht; 2001.View ArticleMATHGoogle 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.1996.0438MathSciNetView ArticleMATHGoogle 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.MathSciNetMATHGoogle Scholar
  5. Kirk WA, Shin SS: Fixed point theorems in hyperconvex spaces. Houston Journal of Mathematics 1997,23(1):175–188.MathSciNetMATHGoogle 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)00456-3MathSciNetView ArticleMATHGoogle 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. 10.1080/01630569908816911MathSciNetView ArticleMATHGoogle 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.1996.0014MathSciNetView ArticleMATHGoogle 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.1997.5388MathSciNetView ArticleMATHGoogle 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

Copyright

© Zoran D. Mitrović 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.