Advanced search    

Search: authors:"Tomasz Szostok"

6 papers found.
Use AND, OR, NOT, +word, -word, "long phrase", (parentheses) to fine-tune your search.

On an Equation of Sophie Germain

, Justyna Sikorska and Tomasz Szostok Institute of Mathematics University of Silesia ul. Bankowa 14 40-007 Katowice Poland e-mail: [1] Acz´el, J.: A mean value property of the derivative of quadratic

Functional Inequalities Involving Numerical Differentiation Formulas of Order Two

Introduction Writing the celebrated Hermite–Hadamard inequality f (t )dt ≤ B Tomasz Szostok in the form F (y) − F (x ) y − x y − x Remark 1 Let f, F, : [x , y] → R be such that = F, F = f, let ni , mi ∈ N

Stability of functional equations connected with quadrature rules

We study the stability properties of the equation $$F(y) - F(x) = (y - x) \sum_{i=1}^{n}a_{i}f(\alpha_i x + \beta_{i}y)$$ (0.1)which is motivated by numerical integration. In Szostok and Wa̧sowicz (Appl Math Lett 24(4):541–544, 2011) the stability of the simplest equation of the type (0.1) was investigated thus the inequality $$\left|F(y) - F(x) - (y - x)f\left(x + y\right)\right...

Ohlin’s lemma and some inequalities of the Hermite–Hadamard type

Tomasz Szostok 0 0 Tomasz Szostok Institute of Mathematics University of Silesia Bankowa 14 40-007 Katowice Poland Using the Ohlin lemma on convex stochastic ordering we prove inequalities of the

Inequalities of the Hermite–Hadamard Type Involving Numerical Differentiation Formulas

permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. Andrzej Olbrys and Tomasz Szostok Institute of Mathematics Bankowa 14 40-007

On a modified version of Jensen inequality

On a Modified Version of Jensen Inequality TOMASZ SZOSTOK 0 1 0 AMS Subject Classification: 39B22 , 39B72 1 Institute of Mathematics, Silesian University , Bankowa 14, 40-007 Katowice , Poland