×

Approximation by complex \(q\)-Szász-Kantorovich operators in compact disks, \(q>1\). (English) Zbl 1286.41004

Summary: In this paper, the exact order \(\frac{1}{q^n}\), \(q>1\), in approximation and Voronovskaja-type results for the complex \(q\)-Szász-Kantorovich operators attached to analytic functions on compact disks are obtained.

MSC:

41A25 Rate of convergence, degree of approximation
30E10 Approximation in the complex plane
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Favard, J.: Sur les multiplicateurs d’interpolation. J. Math. Pures Appl. 23(Series 9), 219–247 (1944) · Zbl 0063.01317
[2] Gal, S.G.: Approximation by Complex Bernstein and Convolution Type Operators. World Scientific, New Jersey (2009) · Zbl 1237.41001
[3] Gal, S.G.: Approximation and geometric properties of complex Favard-Szasz-Mirakian operators in compact diks. Comput. Math. Appl. 56, 1121–1127 (2008) · Zbl 1155.41303 · doi:10.1016/j.camwa.2008.02.014
[4] Gal, S.G.: Approximation of analytic functions without exponential growth conditions by complex Favard-Szász-Mirakjan operators. Rendiconti del Circolo Matematico di Palermo 59(3), 367–376 (2010) · Zbl 1207.30056 · doi:10.1007/s12215-010-0028-9
[5] Kac, V., Cheung, P.: Quantum Calculus. Universitext. Springer, New York (2002) · Zbl 0986.05001
[6] Mahmudov, N.I.: Approximation properties of complex $$q$$ -Szász-Mirakjan operators in compact disks. Comput. Math. Appl. 60, 1784–1791 (2010) · Zbl 1202.30061 · doi:10.1016/j.camwa.2010.07.009
[7] Totik, V.: Uniform approximation by positive operators on infinite intervals. Anal. Math. 10, 163–182 (1984) · Zbl 0579.41015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.