Probabilistic characterization of strong convexity

• Autorzy: Rajba T. , Wąsowicz S.
• Języki publikacji: EN

Abstrakty

EN

Strong convexity is considered for real functions defined on a real interval. Probabilistic characterization is given and its geometrical sense is explained. Using this characterization some inequalities of Jensen-type are obtained.

Słowa kluczowe

EN

convexity; strong convexity; Jensen's inequality; Jensen gap of a function; distribution of a random variable; variance

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 1
• Strony: 97--103
• Opis fizyczny: Bibliogr. 6 poz., wykr.

Twórcy

autor

Rajba T.

autor

Wąsowicz S.

• University of Bielsko-Biała Department of Mathematics and Computer Science Willowa 2, 43-309 Bielsko-Biała, Poland,

Bibliografia

• [1] E.F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937), 363-371.
• [2] P. Billingsley, Probability and Measure, John Wiley & Sons, New York, 1995.
• [3] J.B. Hiriart-Urruty, C. Lemaréchal, Fundamentals of convex analysis, Springer-Verlag, Berlin, Heidelberg 2001.
• [4] N. Merentes, K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010), 193-199.
• [5] K. Nikodem, Zs. Páles, Characterizations of inner product spaces by strongly convex functions, Banach J. Math. Anal. 5 (2011) 1, 83-87.
• [6] A.W. Roberts, D.E. Varberg, Convex Functions, Academic Press, New York-London, 1973.