17 citations · 45 across the 14 of their papers we have counts for
15 papers
Refined Gauss--Lobatto bounds for odd-order convexity
Tomasz Kania, Szymon Wąsowicz
For functions that are convex of higher order, classical extremalities identify Gaussian quadrature as a lower bound and Gauss--Lobatto quadrature as an upper bound for the integra…
Adaptive integration of 5-convex and 5-concave functions
Szymon Wąsowicz
An adaptive method connected with 3-point Gauss quadrature and 4-point Lobatto quadrature is introduced and investigated for 5-convex functions.
Inequalities between remainders of quadratures
Andrzej Komisarski, Szymon Wąsowicz
It is well-known that in the class of convex functions the (nonnegative) remainder of the Midpoint Rule of the approximate integration is majorized by the remainder of the Trapezoi…
On the classes of higher-order Jensen-convex functions and Wright-convex functions, II
Jacek Mrowiec, Teresa Rajba, Szymon Wąsowicz
Recently Nikodem, Rajba and Wąsowicz compared the classes of n-Wright-convex functions and n-Jensen-convex functions by showing that the first one is a proper subclass of the latte…
A solution to the problem of Rasa connected with Bernstein polynomials
Jacek Mrowiec, Teresa Rajba, Szymon Wasowicz
During the Conference on Ulam's Type Stability (Rytro, Poland, 2014), Ioan Rasa recalled his 25-years-old problem concerning some inequality involving the Bernstein polynomials. We…
Extremal measures with prescribed moments
Teresa Rajba, Szymon Wasowicz
In the approximate integration some inequalities between the quadratures and the integrals approximated by them are called \emph{extremalities}. On the other hand, the set of all q…
Hermite-Hadamard type inequalities for Wright-convex functions of several variables
D. Śliwińska, Sz. Wasowicz
We present Hermite--Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on simplices
On the classes of higher-order Jensen-convex functions and Wright-convex functions
Kazimierz Nikodem, Teresa Rajba, Szymon Wasowicz
The classes of n-Wright-convex functions and n-Jensen-convex functions are compared with each other. It is shown that for any odd natural number the first one is the proper sub…
On some inequality of Hermite-Hadamard type
Szymon Wasowicz, Alfred Witkowski
It is well-known that the left term of the classical Hermite-Hadamard inequality is closer to the integral mean value than the right one. We show that in the multivariate case it i…
On affine selections of set-valued functions
Szymon Wasowicz
The main result states that every convex set-valued function defined on a real interval with compact values in a locally convex space, admits an affine selection. In the case if th…
Some properties of generalized higher-order convexity
Szymon Wasowicz
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-typ…
Support-type properties of convex functions of higher order and Hadamard-type inequalities
Szymon Wasowicz
It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a simila…
Polynomial selections and separation by polynomials
Szymon Wasowicz
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main res…
On some extremalities in the approximate integration
Szymon Wasowicz
Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under s…
Hermite-Hadamard-type inequalities in the approximate integration
Szymon Wasowicz
We give a slight extension of the Hermite-Hadamard inequality on simplices and we use it to establish error bounds of the operators connected with the approximate integration.