Inequalities for Convex Functions
We consider inequalities of the form _i=0^ma_iφ (b_i)≥ 0, and we give necessary and sufficient conditions on the nodes b_0,b_1,… ,b_m, and the weights a_i for such an inequality to be true for every real convex function φ. In the case the nodes are integers with b_0 the smallest of them, then _i=0^ma_iφ (b_i)≥ 0 if and only if x^-b_0 _i=0^ma_ix^b_i /(x-1)^2 is a polynomial with positive coefficients. 2010 Mathematics Subject Classification. Primary: 26A24. , number=2, journal=Sarajevo Journal of Mathematics, author=Fejzić, Hajrudin and Živojević, Fuad, year=2024, month=Jun., pages=187–195