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We use Lidstone’s interpolating polynomials to obtain Popoviciu-type inequalities containing sums ∑i=1 pi f (xi) , where f is an n -convex function with even n . We also give integral analogues of the results, some related inequalities for n -convex functions at a point and bounds for integral remainders of identities associated with the obtained inequalities. Mathematics subject classification (2010): 26D15, 26D10.

Popoviciu type inequalities for higher order convex functions via Lidstone interpolation