Opuscula Mathematica
Opuscula Math. 31, no. 1 (2011), 97-103

Probabilistic characterization of strong convexity

Teresa Rajba
Szymon Wąsowicz
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.
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About the authors ▼
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
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Received: 2010-04-23.
Accepted: 2010-06-06.
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Teresa Rajba, Szymon Wąsowicz, Probabilistic characterization of strong convexity, Opuscula Math. 31, no. 1 (2011), 97-103, http://dx.doi.org/10.7494/OpMath.2011.31.1.97.
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