Approximation properties of generalized Jain operators

Abstract

In this paper, we investigate a variant of the Jain operators, which preserve the linear functions. We compute the rate of convergence of these operators with the help of K-functional. We also introduce modifications of the Jain operators based on the models in [4] and [10]. These modified operators yield better error estimates than the Jain operators.

Some approximation properties of a new class of linear operators

“…The generalized Jain operators as variant of the Lupaş operators were studied by Patel and Mishra . Some related work in this area can be found in other works . Motivated by this, we give further modification of Jain operators in this paper with the help of a generalized Poisson‐type distribution, establish its convergence properties, and discuss its degree of approximation, asymptotic formula, and statistical convergence.…”

Kantorovich-type operators associated with a variant of Jain operators

“…This property becomes useful in the study of the approximation properties which the operators enjoy. Pursuing this goal, in [7] the authors introduced and investigated the following variant of Jain operators…”

Approximation properties of a certain nonlinear Durrmeyer operators

“…For future studies, it is important to say that this kind of approach can apply for several linear positive operators presented in the papers [10], [13], [29] and in the very recent books of Gupta-Agarwal [15] (see also Gal [12]).…”