Opuscula Math. 35, no. 3 (2015), 397-410
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.
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- Communicated by Zbigniew Szkutnik.
- Received: 2013-11-16.
- Revised: 2014-09-16.
- Accepted: 2014-09-23.
- Published online: 2014-12-15.