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Approximation of functions of two variables by some operators in weighted spaces. (English) Zbl 0934.41017

The authors study some linear positive operators of Szász-Mirakyan type in polynomial and exponential weighted spaces of continuous functions of two variables. The degree of approximation and the corresponding Voronovskaya formula are investigated. Similar results for functions of one variable have been previously obtained by the authors and M. Skorupka.

MSC:

41A36 Approximation by positive operators
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References:

[1] M. Becker , Global approximation theorems for Szasz-Mirakjan and Baskakov operators in polynomial weight spaces , Indiana Univ. Math. J. , 27 ( 1 ) ( 1978 ), pp. 127 - 142 . MR 493079 | Zbl 0358.41006 · Zbl 0358.41006 · doi:10.1512/iumj.1978.27.27011
[2] M. Becker - D. Kucharski - R.J. Nessel , Global approximation theorems for the Szasz-Mirakjan operators in exponential weight spaces , in Linear Spaces and Approximation (Proc. Conf. Oberwolfach, 1977 ), Birkhäuser Verlag , Basel ISNM , 40 ( 1978 ), pp. 319 - 333 . MR 499919 | Zbl 0386.41014 · Zbl 0386.41014
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[7] L. Rempulska - M. Skorupka , The Vornovkaya theorem for some operators of the Szasz-Mirakjan type , Le Matematiche , 50 ( 2 ) ( 1995 ), pp. 251 - 261 . MR 1414633 | Zbl 0901.41019 · Zbl 0901.41019
[8] L. Rempulska - M. Skorupka , The Bernstein inequality for some operators of the Szasz-Mirakjan type , Note di Matematica , 14 ( 2 ) ( 1994 ), pp. 277 - 290 . MR 1457226 | Zbl 0889.41018 · Zbl 0889.41018
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