1 citations · 1 across the 6 of their papers we have counts for
8 papers
On Popoviciu's concept of convexity for functions of variables
Andrzej Komisarski, Teresa Rajba
We establish an integral representation for Popoviciu's convex functions of variables. This representation serves as a~foundation for deriving several functional inequalities,…
Convex order for convolution polynomials of Borel measures
Andrzej Komisarski, Teresa Rajba
We give necessary and sufficient conditions for Borel measures to satisfy the inequality introduced by Komisarski, Rajba (2018). This inequality is a generalization of the convex o…
A sharpening of a problem on Bernstein polynomials and convex function and related results
Andrzej Komisarski, Teresa Rajba
We present a short proof of a conjecture proposed by I. Raşa (2017), which is an inequality involving basic Bernstein polynomials and convex functions. This proof was given in the…
Muirhead inequality for convex orders and a problem of I. Raşa on Bernstein polynomials
Andrzej Komisarski, Teresa Rajba
We present a new, very short proof of a conjecture by I. Raşa, which is an inequality involving basic Bernstein polynomials and convex functions. It was affirmed positively very re…
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 behavior of integrable functions at infinity
Andrzej Komisarski
We investigate the behavior of sequences for Lebesgue integrable functions . In particular, we give a~description of classes of multipliers $…
Sums of compositions of pairs of projections
Andrzej Komisarski, Adam Paszkiewicz
We give some necessary and sufficient conditions for the possibility to represent a Hermitian operator on an infinite-dimensional Hilbert space (real or complex) in the form $\sum_…
On the stability of the existence of fixed points for the projection-iterative methods with relaxation
Andrzej Komisarski, Adam Paszkiewicz
We consider an -relaxed projection given by where and is the projection onto a non-empty, convex and closed subset …