Approximation Properties of Bivariate Extension of q-Bernstein–Schurer–Kantorovich operators

Results in Mathematics - In this paper, we introduce a bivariate generalization of the Bernstein–Schurer–Kantorovich operators based on q-integers and get a Bohmann–Korovkin type...     

Some approximation properties of a Durrmeyer variant of q‐Bernstein–Schurer operators

In this paper, we will propose a Durrmeyer variant of q‐Bernstein–Schurer operators. A Bohman–Korovkin‐type approximation theorem of these operators is considered. The rate of convergence by using the first modulus of smoothness is computed. The statistical approximation of these operators is also studied. Copyright © 2016 John Wiley & Sons, Ltd.     

Some approximation properties by a class of bivariate operators

Starting with the well‐ known Bernstein operators, in the present paper, we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely, the generalized Boolean sum (GBS) in the Bögel space of continuous functions is given. In order to underline the fact that in this particular case, GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also, the error of approximation for the modified Bernstein operators and its GBS‐type operator are compared.