MMN-2265

# Rate of convergence of q-analogue of a class of new Bernstein type operators

*Sheetal Deshwal*;

*Ana Maria Acu*;

*P. N. Agrawal*;

## Abstract

Sharma [26] introduced a q-analogue of a new sequence of classical Bernstein type operators deﬁned by Deo et al. [12] for functions deﬁned in the interval
[0, n/(n+1)]. The purpose of this paper is to study the rate of convergence of these operators with the aid of the modulus of continuity and a Lipschitz type space. Subsequently, we deﬁne the bivariate case of these operators and discuss the approximation properties by means of the complete and partial modulus of continuity, Lipschitz class and the Peetre’s K-functional. Some numerical results which show the rate of convergence of these operators to certain functions using Maple algorithms are given. Lastly, we construct the associated GBS operators and study the approximation of Bogel continuous and Bogel diﬀerentiable functions. The comparison of convergence of the bivariate operator and its GBS type operator is made considering numerical examples.

Vol. 19 (2018), No. 1, pp. 211-234

DOI: 10.18514/MMN.2018.2265