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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 41 Issue: 5

ON GENERALIZATIONS OF THE CONCEPT OF CONVEXITY

G. Adilov
İ. Yesilce
Sayfa
—
Yayın Tarihi
2012-05-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Horvath, the other being B−1 -convexity which is introduced and examined by us.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this article, the concept of convexity is considered.
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Temel Bulgular & Veri:Generalizations of this concept, that were examined by different authors, are briefly given.
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Sonuç & Katkı:Horvath, the other being B−1 -convexity which is introduced and examined by us.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Abstract convexity · B-convexity · B−1 -convexity

Abstract

In this article, the concept of convexity is considered. Generalizations of this concept, that were examined by different authors, are briefly given. In this paper, a study of two forms of abstract convexity is undertaken: one of which is B-convexity which was defined and analyzed by W. Briec and C. Horvath, the other being B−1 -convexity which is introduced and examined by us.

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Bu Makaleye Atıf Yap

Adilov, G., Yesilce, İ. (2012). ON GENERALIZATIONS OF THE CONCEPT OF CONVEXITY. Hacettepe Journal of Mathematics and Statistics, Volume: 41 Issue: 5. https://ajindex.com/articles/1403519

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Kaynakça (13)

  1. Adilov, G. and Rubinov, A. B-convex sets and functions, Numerical Functional Analysis and Optimization 27 (3-4), 237–257, 2006.
  2. Avriel, M. R-convex functions, Mathematical Programming 2, 309–323, 1972.
  3. Ben-Tal, A. On generalized means and generalized convex functions, Journal of Optimization Theory and Applications 21 (1), 1–13, 1977.
  4. Briec, W. and Horvath, C. D. B-convexity, Optimization 53, 103–127, 2004.
  5. Briec, W. and Horvath, C. D. Halfspaces and Hahn-Banach like properties in B-convexity and Max-Plus convexity, Pacific J. Optim. 4 (2), 293–317, 2008.
  6. Briec, W, Horvath, C. D. and Rubinov, A. M. Separation in B-convexity, Pacific J. Optimiz., 13–30, 2005.
  7. Hadjisavvas, N., Komlosi, S. and Schaible, S. Handbook on Generalized Convexity and Gen- eralized Monotonicity(Springer, New York, 2005).
  8. Kuratowski, K. Topology (Academic Press, New York, 1968).
  9. Rockafellar, R. T. Convex Analysis (Princeton University Press, Princeton, New Jersey, ). Rubinov, A. Abstract Convexity and Global Optimization (Kluwer Academic Publishers, Boston, Dordrecht, London, 2000).
  10. Singer, I. Abstract Convex Analysis (John Wiley & Sons., New York, 1997).
  11. Van De Vel, M. L. J. Theory of Convex Structures (North Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, 1993).
  12. Briec, W, Horvath, C. D. and Rubinov, A. M. Separation in B-convexity, Pacific J. Optimiz., 13–30, 2005.
  13. Van De Vel, M. L. J. Theory of Convex Structures (North Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, 1993).