Some properties of qBernsteinDurrmeyer operators
H. Karsli
In the present paper we shall
investigate the pointwise approximation properties of the q analogue of the
BernsteinDurrmeyer operators and estimate the rate of pointwise convergence
of these operators to the functions $f$ whose qderivatives are bounded
variation on the interval $[0,1].$ We give an estimate for the rate of
convergence of the operator $\left( L_{n,q}f\right) $
at those points $x$ at which the one sided qderivatives $D_{q}^{+} f(x),D_{q}^{} f(x)$
exist. We shall also prove that the operators $L_{n,q}f$
converges to the limit $f(x).$ To the best of my knowledge, the present
study will be the first study on the approximation of q operators in the
space of $ D_{q}BV$.
Tbilisi Mathematical Journal, Vol. 12(4) (2019), pp. 189204
