Abstract
In this paper, the exact order of simultaneous approximation and Voronovskaja kind results with quantitative estimate for the complex Beta operators of first kind attached to analytic functions in strips of compact disks are obtained. In this way, we put in evidence the overconvergence phenomenon for this operator, namely the extensions of approximation properties with upper and exact quantitative estimates, from the real interval (0, 1) to strips in compact disks of the complex plane of the form \({SD^{r}(0, 1) = \{z \in \mathbb{C}; |z| \leq r, 0 < Re(z) < 1\}}\)and \({SD^{r}[a, b] = \{z \in \mathbb{C}; |z| \leq r, a \leq Re(z) \leq b\}}\), with r ≥ 1 and 0 < a < b < 1.
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Dedicated to the 60th birthday of professor Francesco Altomare
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Gal, S.G., Gupta, V. Approximation by Complex Beta Operators of First Kind in Strips of Compact Disks. Mediterr. J. Math. 10, 31–39 (2013). https://doi.org/10.1007/s00009-011-0164-2
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DOI: https://doi.org/10.1007/s00009-011-0164-2