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A NOTE ON PRECONVEXITY SPACES

  • Received : 2007.08.28
  • Accepted : 2007.10.01
  • Published : 2007.12.25

Abstract

In this paper, we introduce the concepts of the convexity hull and co-convex sets on preconvexity spaces. We study some properties for the co-convexity hull and characterize c-convex functions and c-concave functions by using the co-convexity hull and the convexity hull.

Keywords

preconvexity;co-convex sets;co-convexity hull;c-convex function;c-concave function

References

  1. W. K. Min, Some results on preconvexity spaces, (submitted).
  2. M. D. Guay, An introduction to preconvexity spaces, Acta Math. Hungar., vol. 105 (3)(2004), pp. 241-248. https://doi.org/10.1023/B:AMHU.0000049290.67473.2c
  3. S. A. Naimpally and B. D. Warrack, Proximity spaces, Cambridge University Press (1970).

Cited by

  1. p-PRECONVEX SETS ON PRECONVEXITY SPACES vol.30, pp.3, 2008, https://doi.org/10.5831/HMJ.2008.30.3.425