Abstract
AbstractWe prove that various Durrmeyer-type operators preserve q-monotonicity in [0, 1] or $$[0,\infty )$$
[
0
,
∞
)
as the case may be. Recall that a 1-monotone function is nondecreasing, a 2-monotone one is convex, and for $$q>2$$
q
>
2
, a q-monotone function possesses a convex $$(q-2)$$
(
q
-
2
)
nd derivative in the interior of the interval. The operators are the Durrmeyer versions of Bernstein (including genuine Bernstein–Durrmeyer), Szász and Baskakov operators. As a byproduct we have a new type of characterization of continuous q-monotone functions by the behavior of the integrals of the function with respect to measures that are related to the fundamental polynomials of the operators.
Funder
Technische Hochschule Mittelhessen
Publisher
Springer Science and Business Media LLC
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