On error bounds for Gauss-Legendre and Lobatto quadrature rules.
Inequalities between the quadrature operators and error bounds of quadrature rules.
A new proof of some inequality connected with quadratures.
On quadrature rules, inequalities and error bounds.
Polynomial selections and separation by polynomials
K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
A sandwich theorem and Hyers-Ulam stability of affine functions.
Abstract separation theorems of Rodé type and their applications
Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.
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