POPOVICIU TYPE INEQUALITIES FOR HIGHER ORDER CONVEX FUNCTIONS VIA LIDSTONE INTERPOLATION

We use Lidstone's interpolating polynomials to obtain Popoviciu-type inequalities containing sums Sigma(m)(i=1) p(i)f(x(i)) , 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.