Approximation by certain linear positive operators of two variables. (English) Zbl 1474.41052

Summary: We introduce positive linear operators which are combined with the Chlodowsky and Szász type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by means of the modulus of continuity. And we also obtain weighted approximation properties for these positive linear operators in a weighted space of functions of two variables and find the convergence rate for these operators by using the weighted modulus of continuity.


41A36 Approximation by positive operators
41A10 Approximation by polynomials
41A63 Multidimensional problems
Full Text: DOI


[1] Gadjiev, A. D.; Efendiev, R. O.; Ibikli, E., Generalized Bernstein-Chlodowsky polynomials, The Rocky Mountain Journal of Mathematics, 28, 4, 1267-1277 (1998) · Zbl 0927.41018 · doi:10.1216/rmjm/1181071716
[2] Gadjieva, E. A.; Ibikli, E., On generalization of Bernstein-Chlodowsky polynomials, Hacettepe Bulletin of Natural Sciences and Engineering, 24, 31-340 (1995) · Zbl 0861.41017
[3] Mursaleen, M.; Khan, A., Generalized \(q\)-Bernstein-Schurer operators and some approximation theorems, Journal of Function Spaces and Applications, 2013 (2013) · Zbl 1291.41020 · doi:10.1155/2013/719834
[4] Mursaleen, M.; Khan, F.; Khan, A., Statistical approximation for new positive linear operators of Lagrange type, Applied Mathematics and Computation, 232, 548-558 (2014) · Zbl 1410.40005 · doi:10.1016/j.amc.2014.01.093
[5] Walczak, Z., On certain modified Szász-Mirakyan operators for functions of two variables, Demonstratio Mathematica, 33, 1, 91-100 (2000) · Zbl 0960.41016
[6] İspir, N.; Atakut, Ç., Approximation by modified Szasz-Mirakjan operators on weighted spaces, Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 112, 4, 571-578 (2002) · Zbl 1011.41012 · doi:10.1007/BF02829690
[7] Taşdelen, F.; Olgun, A.; Başcanbaz-Tunca, G., Approximation of functions of two variables by certain linear positive operators, Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 117, 3, 387-399 (2007) · Zbl 1151.41014 · doi:10.1007/s12044-007-0033-x
[8] Volkov, V. I., On the convergence of sequences of linear positive operators in the space of continuous functions of two variable, Matematicheskii Sbornik, 43, 85, 504 (1957)
[9] Gadjiev, A. D., Linear Positive Operators in Weighted Space of Functions of Several Variables (1980), Izvestiya Academy of Sciences of Azerbaijan
[10] Gadjiev, A. D.; Hacısalihoğlu, H., Convergence of the Sequences of Linear Positive Operators, Ankara, Turkey: Ankara University Press, Ankara, Turkey
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.