Opuscula Mathematica
Opuscula Math. 35, no. 3 (), 397-410
Opuscula Mathematica

Generalized Levinson's inequality and exponential convexity

Abstract. We give a probabilistic version of Levinson's inequality under Mercer's assumption of equal variances for the family of 3-convex functions at a point. We also show that this is the largest family of continuous functions for which the inequality holds. New families of exponentially convex functions and related results are derived from the obtained inequality.
Keywords: Levinson's inequality, exponential convexity.
Mathematics Subject Classification: 26D15.
Cite this article as:
Josip Pečarić, Marjan Praljak, Alfred Witkowski, Generalized Levinson's inequality and exponential convexity, Opuscula Math. 35, no. 3 (2015), 397-410, http://dx.doi.org/10.7494/OpMath.2015.35.3.397
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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