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

Sheetal Deshwal; Ana Maria Acu; P. N. Agrawal;


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

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