Tomasz Szostok

activity

20142023

most citedLevin Steckin theorem and inequalities of the Hermite-Hadamard type

7 citations · 9 across the 4 of their papers we have counts for

collaborators

4 papers

math.CA2023★ 1 cited

A generalization of a theorem of Brass and Schmeisser

Tomasz Szostok

Let $n$ be an odd positive integer. It was proved by Brass and Schmeisser that for every quadrature $Q = α_{1} f (x_{1}) + \dots + α_{m} f (x_{m}),$ (with positive weights) of order at l…

math.CA2016

Functional inequalities involving numerical differentiation formulas of order two

Tomasz Szostok

We write expressions connected with numerical differentiation formulas of order $2$ in the form of Stieltjes integral, then we use Ohlin lemma and Levin-Stechkin theorem to study i…

math.CA2014★ 1 cited

Inequalities of the Hermite-Hadamard type involving numerical differentiation formulas

Andrzej Olbryś, Tomasz Szostok

We observe that the Hermite-Hadamard inequality written in the form $f (\frac{x + y}{2}) \leq \frac{F ( y ) - F ( x )}{y - x} \leq \frac{f ( x ) + f ( y )}{2}$ may be viewed as an inequality b…

math.CA2014★ 7 cited

Levin Steckin theorem and inequalities of the Hermite-Hadamard type

Tomasz Szostok

Recently Ohlin lemma on convex stochastic ordering was used to obtain some inequalities of Hermite-Hadamard type. Continuing this idea, we use Levin-Stečkin result to determine all…