Opuscula Math. 31, no. 1 (2011), 97-103
http://dx.doi.org/10.7494/OpMath.2011.31.1.97
Opuscula Mathematica
Probabilistic characterization of strong convexity
Abstract. 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.
Keywords: convexity, strong convexity, Jensen's inequality, Jensen gap of a function, distribution of a random variable, variance.
Mathematics Subject Classification: 26A51, 26D15, 60E05, 60E15.
- Teresa Rajba
- University of Bielsko-Biała, Department of Mathematics and Computer Science, Willowa 2, 43-309 Bielsko-Biała, Poland
- Szymon Wąsowicz
- University of Bielsko-Biała, Department of Mathematics and Computer Science, Willowa 2, 43-309 Bielsko-Biała, Poland
- Received: 2010-04-23.
- Accepted: 2010-06-06.
