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Converses of the Jensen Inequality for (2m)-convex Functions and Completely Convex Functions

In this note we consider (2m)-convex functions and completely convex functions. Using the ineterpolating polynomials (hermite's and Lindstone's interpolating polynomials) and conditions on the Green's functions the results concering for the converses of the Jensen inequality for signed measure are presented.

Green function, Jensen inequality, (2m)-convex function, completely convex function, Lidstone polynomial, Hermite polynomial

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