충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제23권3호
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  • Pages.481-486
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  • 2010
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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STRONGLY C-CONVEX FUNCTIONS AND ALMOST C-CONVEX FUNCTIONS ON PRECONVEXITY SPACES

  • Min, Won Keun (Department of Mathematics Kangwon National University)
  • 투고 : 2010.04.30
  • 심사 : 2010.08.12
  • 발행 : 2010.09.30
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초록

In this paper, we introduce the concepts of strongly c-convex( strongly c-concave) function, almost c-convex function on preconvex spaces. We investigate the relationships between such concepts and several types of preconvex sets.

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참고문헌

  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, A Note on preconvexity spaces, Honam Mathmatical Journal, 29 (2007), no. 4, 589-595. https://doi.org/10.5831/HMJ.2007.29.4.589
  3. W. K. Min, Some results on preconvexity spaces, Bull. Korean Math. Soc. 45 (2008), no. 1, 39-41. https://doi.org/10.4134/BKMS.2008.45.1.039
  4. W. K. Min, $\rho$-Preconvex set on preconvexity spaces, Honam Mathmatical Journal 30 (2008), no. 3, 589-595. https://doi.org/10.5831/HMJ.2008.30.4.589
  5. W. K. Min, Semi-preconvex set on preconvexity spaces, Commun. Korean Math. Soc. 23 (2008), no. 2, 251-256. https://doi.org/10.4134/CKMS.2008.23.2.251
  6. W. K. Min, $\alpha$-preconvex set on preconvexity spaces, Korean Annals of Mathematics 26 (2009), no 1-2, 5-11.
  7. W. K. Min, $\beta$-preconvex set on preconvexity spaces, Commun. Korean Math. Soc. 25 (2010), no. 1, 105-110. https://doi.org/10.4134/CKMS.2010.25.1.105
  8. S. A. Naimpally and B. D. Warrack, Proximity spaces, Cambridge University Press, 1970.