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Some properties of the generalized Bleimann, Butzer and Hahn operators. (English) Zbl 1354.41023

Summary: In the present paper, we introduce sequences of Bleimann, Butzer and Hahn operators which are based on a function \(\tau\). This function is a continuously differentiable function on \(\mathbb{R}^+\), such that \(\tau(0)=0\), \(\inf \tau'(x)\geq 1\). We give a Korovkin-type theorem and prove uniform approximation of the generalized Bleimann, Butzer and Hahn operator. We also investigate the monotonic convergence property of the sequence of the operators under \(\tau\)-convexity.

MSC:

41A36 Approximation by positive operators
41A20 Approximation by rational functions
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