Parametric generalization of the modified Bernstein-Kantorovich operators

Abstract

In the current article, a parametrization of the modified Bernstein-Kantorovich operators is studied. Then the Korovkin theorem, approximation properties and central moments of these operators are investigated. The rate of approximation of the operators is obtained by the help of modulus of continuity, functions from Lipschitz class and Peetre-$\mathcal{K}$ functional. Finally, some numerical examples are illustrated to show the effectiveness of the newly defined operators.

Keywords

• Bernstein-Kantorovich operators
• Peetre-K functional
• modulus of continuity
• Lipschitz class

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