2014/11/28 by Andrzej Olbryś, Olbryś, Andrzej, Tomasz Szostok +1
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Matrix Theory and Algorithms #math.CA
paper · pdf · doi:10.48550/arxiv.1411.7859
arxiv created 2014/11/28 · openalex publication_date 2014/11/28 · arxiv updated 2014/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We observe that the Hermite-Hadamard inequality written in the form f((x+y)/(2))≤(F(y)-F(x))/(y-x)≤(f(x)+f(y))/(2) may be viewed as an inequality between two quadrature operators f((x+y)/(2)) (f(x)+f(y))/(2) and a differentiation formula (F(y)-F(x))/(y-x). We extend this inequality, replacing the middle term by more complicated ones. As it turns out in some cases it suffices to use Ohlin lemma as it was done in a recent paper \citeRajba however to get more interesting result some more general tool must be used. To this end we use Levin-Stečkin theorem which provides necessary and sufficient conditions under which inequalities of the type we consider are satisfied.