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MKZ type operators providing a better estimation on \([1/2,1)\). (English) Zbl 1132.41318

Summary: We introduce a modification of the Meyer-König and Zeller (MKZ) operators which preserve the test functions \(f_0(x) = 1\) and \(f_2(x)= x^2\), and we show that this modification provides a better estimation than the classical MKZ operators on the interval \([1/2, 1)\) with respect to the modulus of continuity and the Lipschitz class functionals. Furthermore, we present the \(r\)-th order generalization of our operators and study their approximation properties.

MSC:

41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
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