17 citations · 45 across the 14 of their papers we have counts for
6 papers · 2 filters
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.