MMN-4847
Hermite-Hadamard type inequalities by using Newton-Cotes quadrature formulas
Angshuman R. Goswami; Ferenc Hartung;Abstract
A convex function $f:[a,b]\to\R$ satisfies the so-called Hermite-Hadamard inequality
$$
f\bigg(\dfrac{a+b}{2}\bigg)\leq \frac{1}{b-a}\int_a^{b}f(t)dt\leq \dfrac{f(a)+f(b)}{2}.
$$
Motivated by the above estimates, in this paper we consider approximately monotone and convex functions, and give upper and lower bounds to the numerical integral mean, i.e., to $\frac1{b-a}\mathcal{I}_{n}(f)$, where $\mathcal{I}_{n}(f)$
denotes some of the most popular Newton-Cotes quadrature formulas.
Vol. 26 (2025), No. 1, pp. 261-273