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Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 5

ON GENERALIZATIONS OF THE CONCEPT OF CONVEXITY

G. ADILOV
I. YESILCE
Pages
723–730
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, the concept of convexity is considered.
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Key Findings & Data:Generalizations of this concept, that were examined by different authors, are briefly given.
💡
Conclusion & Impact:Horvath, the other being B−1 -convexity which is introduced and examined by us.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article

ADILOV, G., YESILCE, I. (2022). ON GENERALIZATIONS OF THE CONCEPT OF CONVEXITY. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 5, 723–730. https://ajindex.com/articles/530496

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References (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,
  10. Princeton, New Jersey, ). Rubinov, A. Abstract Convexity and Global Optimization (Kluwer Academic Publishers,
  11. Boston, Dordrecht, London, 2000).
  12. Singer, I. Abstract Convex Analysis (John Wiley & Sons., New York, 1997).
  13. Van De Vel, M. L. J. Theory of Convex Structures (North Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, 1993).