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Cauchy's error representation of Lidstone interpolating polynomial and related results

In this paper we consider the Cauchy’s error representation of Lidstone interpolating polynomial and as a consequence the results concerning to the Hermite-Hadamard inequalities. Using these inequalities, we produce new exponentially convex functions. Also, we give several examples of the families of functions for which the obtained results can be applied.

Green function; (2n)-convex function; Lidstone polynomial; Cauchy type mean value theorems; Hermite-Hadamard inequality; n-exponential convexity; exponential convexity; log-convexity; means

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