Skip to content


  • Research Article
  • Open Access

On almost coincidence points in generalized convex spaces

Fixed Point Theory and Applications20062006:91397

  • Received: 19 April 2006
  • Accepted: 7 June 2006
  • Published:


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.


  • Point Theorem
  • Differential Geometry
  • Maximal Element
  • Computational Biology
  • Convex Space


Authors’ Affiliations

Faculty of Electrical Engineering, University of Banja Luka, Patre 5, Banja Luka, 78000, Bosnia and Herzegovina


  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