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Interpolating polynomials and derived inequalities for convex functions

Using interpolating polynomials and conditions on the Green's functions, and also using Euler's identity, generalizations of Jensen's onequality and converses of Jensen's inequality for regular, real (signed) Borel measure are obtained, and as a consequence Hermite-Hadamard inequalities are presented. Considering Cauchy's error representation of interpolating polynomials, corresponding generalizations of the Hermite-Hadamard inequality are also attained, and as a special case, generalization of the Hermite-Hadamard inequality for the zeros of orthogonal polynomials are considered.

Jensen inequality, Hermite-Hadamard inequality, interpolating polynomials, convex function

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