First-order absolute moment of Meyer-König and Zeller operators and their approximation for some absolutely continuous functions. (English) Zbl 1265.41059
Summary: A sharp estimate is given for the first-order absolute moment of Meyer-König and Zeller operators \(M_{n}\). This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators \(M_{n}\). The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible.
MSC:
| 41A36 | Approximation by positive operators |
| 41A25 | Rate of convergence, degree of approximation |
| 41A10 | Approximation by polynomials |
Keywords:
absolute moment; Meyer-König and Zeller operators; approximation; absolutely continuous functionsReferences:
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