Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SEMI-PRECONVEX SETS ON PRECONVEXITY SPACES

  • Min, Won-Keun (Department of Mathematics Kangwon National University)
  • Published : 2008.04.30
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Abstract

In this paper, we introduce the concept of the semi-preconvex set on preconvexity spaces. We study some properties for the semi-preconvex set. Also we introduce the concepts of the sc-convex function and $s^*c$-convex function. Finally, we characterize sc-convex functions, $s^*$-convex functions and semi-preconvex sets by using the co-convexity hull and the convexity hull.

Keywords

References

  1. M. D. Guay, An introduction to preconvexity spaces, Acta Math. Hungar. 105 (2004), no. 3, 241-248 https://doi.org/10.1023/B:AMHU.0000049290.67473.2c
  2. W. K. Min, Some results on preconvexity spaces, Bull. Korean Math. Soc. 45 (2008), no. 1, 39-44 https://doi.org/10.4134/BKMS.2008.45.1.039
  3. W. K. Min, A note on preconvexity spaces, Honam Math. J. 29 (2007), no. 4, 589-595 https://doi.org/10.5831/HMJ.2007.29.4.589
  4. S. A. Naimpally and B. D.Warrack, Proximity spaces, Cambridge University Press (1970)

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  1. ON PERMUTING 3-DERIVATIONS AND COMMUTATIVITY IN PRIME NEAR-RINGS vol.25, pp.1, 2010, https://doi.org/10.4134/CKMS.2010.25.1.001
  2. p-PRECONVEX SETS ON PRECONVEXITY SPACES vol.30, pp.3, 2008, https://doi.org/10.5831/HMJ.2008.30.3.425
  3. β-PRECONVEX SETS ON PRECONVEXITY SPACES vol.25, pp.1, 2010, https://doi.org/10.4134/CKMS.2010.25.1.105