Yıl: 2012 Cilt: 41 Sayı: 5 Sayfa Aralığı: 723 - 730 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

On generalizations of the concept of convexity

Öz:
In this article, the concept of convexity is considered. Gen eralizations of this concept, that were examined by different authors, are br iefly given. In this paper, a study of two forms of abstract convexity is un dertaken: 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.
Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [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. 1, 13–30, 2005.
  • [7] Hadjisavvas, N., Komlosi, S. and Schaible, S.Handbook on Generalized Convexity and Generalized 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, 1970).
  • [10] Rubinov, A.Abstract Convexity and Global Optimization (Kluwer Academic Publishers, Boston, Dordrecht, London, 2000).
  • [11] Singer, I.Abstract Convex Analysis (John Wiley & Sons., New York, 1997).
  • [12] Van De Vel, M.L.J.Theory of Convex Structures (North Holland Mathematical Library 50, North-Holland Publishing Co., Amsterdam, 1993).
APA ADILOV G, YESILCE I (2012). On generalizations of the concept of convexity. , 723 - 730.
Chicago ADILOV G.,YESILCE I. On generalizations of the concept of convexity. (2012): 723 - 730.
MLA ADILOV G.,YESILCE I. On generalizations of the concept of convexity. , 2012, ss.723 - 730.
AMA ADILOV G,YESILCE I On generalizations of the concept of convexity. . 2012; 723 - 730.
Vancouver ADILOV G,YESILCE I On generalizations of the concept of convexity. . 2012; 723 - 730.
IEEE ADILOV G,YESILCE I "On generalizations of the concept of convexity." , ss.723 - 730, 2012.
ISNAD ADILOV, G. - YESILCE, I.. "On generalizations of the concept of convexity". (2012), 723-730.
APA ADILOV G, YESILCE I (2012). On generalizations of the concept of convexity. Hacettepe Journal of Mathematics and Statistics, 41(5), 723 - 730.
Chicago ADILOV G.,YESILCE I. On generalizations of the concept of convexity. Hacettepe Journal of Mathematics and Statistics 41, no.5 (2012): 723 - 730.
MLA ADILOV G.,YESILCE I. On generalizations of the concept of convexity. Hacettepe Journal of Mathematics and Statistics, vol.41, no.5, 2012, ss.723 - 730.
AMA ADILOV G,YESILCE I On generalizations of the concept of convexity. Hacettepe Journal of Mathematics and Statistics. 2012; 41(5): 723 - 730.
Vancouver ADILOV G,YESILCE I On generalizations of the concept of convexity. Hacettepe Journal of Mathematics and Statistics. 2012; 41(5): 723 - 730.
IEEE ADILOV G,YESILCE I "On generalizations of the concept of convexity." Hacettepe Journal of Mathematics and Statistics, 41, ss.723 - 730, 2012.
ISNAD ADILOV, G. - YESILCE, I.. "On generalizations of the concept of convexity". Hacettepe Journal of Mathematics and Statistics 41/5 (2012), 723-730.