The purpose of this paper is to introduce a Kantorovich variant of Lupa\c{s}-Stancu operators based on Polya distribution with Pochhammer $k$-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function $f$ is better than that of some other operators in a certain range of values of $k$.
Bernstein operators Stancu operators Lupas operators Kantorovich operators Polya distribution modulus of continuity Lipschitz class Voronovskaja type theorem Pochhammer k-symbol
Scientific Research Projects Coordination Unit of Kırıkkale University
Project number 2020/045
Project number 2020/045
Primary Language | English |
---|---|
Subjects | Mathematical Sciences |
Journal Section | Mathematics |
Authors | |
Project Number | Project number 2020/045 |
Publication Date | April 1, 2022 |
Published in Issue | Year 2022 Volume: 51 Issue: 2 |