On Kantorovich variant of Brass-Stancu operators. (English) Zbl 07899337
Summary: In this study, we deal with Kantorovich-type generalization of the Brass-Stancu operators. For the sequence of these operators, we study \(L^p\)-convergence and give some upper estimates for the \(L^p\)-norm of the approximation error via first-order averaged modulus of smoothness and the first-order \(K\)-functional. Moreover, we show that the Kantorovich generalization of each Brass-Stancu operator satisfies variation detracting property and is bounded with respect to the norm of the space of functions of bounded variation on \([0, 1]\). Finally, we present graphical and numerical examples to compare the convergence of these operators to given functions under different parameters.
MSC:
| 41A36 | Approximation by positive operators |
| 41A25 | Rate of convergence, degree of approximation |
| 26A45 | Functions of bounded variation, generalizations |
Keywords:
Brass-Stancu-Kantorovich operators; \(L^p\)-convergence; averaged modulus of smoothness; \(K\)-functional; variation detracting propertyReferences:
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