q-Durrmeyer operators based on Pólya distribution

Abstract

We introduce a q analogue of Durrmeyer type modification of Bernstein operators based on Pólya distributions. We study the ordinary approximation properties of operators using modulus of continuity and Peetre K-functional of second order. Further, we establish the weighted approximation properties for these operators.

Degree of approximation for bivariate extension of blending type q -Durrmeyer operators based on Pólya distribution

“…Motivated by Gupta et al [10], for h ∈ C(I 2 ) and 0 < q m 1 , q m 2 < 1, we construct the bivariate extension of the univariate q-Durrmeyer operators based Pólya distribution for each positive integers m 1 , m 2 as follows:…”

“…In [10], the q-Durrmayer type modification of operator (1.2) was introduced and studied by Gupta et al The q-Durrmeyer type operator based on Pólya distribution was defined by…”

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

“…Very recently, Gupta et al . introduced a q ‐analogue of a Durrmeyer modification of Bernstein type operators based on Pólya distribution and studied the degree of approximation by means of Peetre's K ‐functional and the weighted approximation properties. Acu et al .…”