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Jensen-type inequalities on time scales for n-convex functions

By utilizing some scalar inequalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Jensen's inequality and in the Edmundson-Lah-Ribaric inequality in time scale calculus that hold for the class of n-convex functions. Main results are then applied to generalized means, with a particular emphasis to power means, and in that way some new reverse relations for generalized and power means that correspond to n-convex functions are obtained.

Time scale ; linear functional ; Jensen's inequality ; n-convex functions ; means

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