This paper aims to two-dimensional extension of some univariate positive approximation processes expressed by series. To be easier to use, we also modify this extension into finite sums. With respect to these two new classes designed, we investigate their approximation properties in polynomial weighted spaces. The rate of convergence is established, and special cases of our construction are highlighted.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
O. Agratini, Bivariate positive operators in polynomial weighted spaces, Abstract and Applied Analysis, 2013, 8 pages, art. id. 850760, https://doi.org/10.1155/2013/850760
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Abstract and Applied Analysis
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 J. Grof, Uber approximation durch polynome mit belegungsfunktion, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 35, no. 1-2, pp. 109–116, 1980.
 H.G. Lehnhoff, “On amodified Szasz-Mirakjan-operator,” Journal of Approximation Theory, vol. 42, no. 3, pp. 278–282, 1984.
 O. Agratini, “On the convergence of a truncated class of operators,” Bulletin of the Institute of Mathematics. Academia Sinica, vol. 31, no. 3, pp. 213–223, 2003.
 G. A. Anastassiou and S. G. Gal, Approximation Theory. Moduli of Continuity and Global Smoothness Preservation, Birkhauser, Boston, Mass, USA, 2000.
 V. A. Baskakov, “An example of a sequence of linear positive operators in the space of continuous functions,” Doklady Akademii Nauk SSSR, vol. 113, pp. 249–251, 1957.
 M. Becker, “Global approximation theorems for Szasz-Mirakjan and Baskakov operators in polynomial weight spaces,” Indiana University Mathematics Journal, vol. 27, no. 1, pp. 127–142, 1978.
 M. Gurdek, L. Rempulska, and M. Skorupka, “The Baskakov operators for functions of two variables,” Collectanea Mathematica, vol. 50, no. 3, pp. 289–302, 1999.
 J. Wang and S. Zhou, “On the convergence of modified Baskakov operators,” Bulletin of the Institute of Mathematics. Academia Sinica, vol. 28, no. 2, pp. 117–123, 2000.
 Z. Walczak, “Baskakov type operators,” The Rocky Mountain Journal of Mathematics, vol. 39, no. 3, pp. 981–993, 2009.
 O. Szasz, “Generalization of S. Bernstein’s polynomials to the infinite interval,” Journal of Research of the National Bureau of Standards, vol. 45, pp. 239–245, 1950.
 Z. Ditzian and V. Totik, Moduli of Smoothness, vol. 9, Springer, New York, NY, USA, 1987.
 N. Ispir and C. Atakut, “Approximation by modified Szasz-Mirakjan operators on weighted spaces,” Proceedings of the Indian Academy of Sciences, vol. 112, no. 4, pp. 571–578, 2002.
 N. I. Mahmudov, “Approximation by the q-Szasz-Mirakjan operators,” Abstract and Applied Analysis, vol. 2012, Article ID 754217, 16 pages, 2012.
 A. Aral, “A generalization of Szasz-Mirakyan operators based on q-integers,” Mathematical and Computer Modelling, vol. 47, no. 9-10, pp. 1052–1062, 2008.
 A. Aral and V. Gupta, “The q-derivative and applications to q-Szasz Mirakyan operators,” Calcolo, vol. 43, no. 3, pp. 151–170, 2006