Approximation properties of some operators in weighted spaces of functions of two variables |
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| Author |
Institute of Mathematics, Poznań University of TechnilogyPiotrowo 3A, 60–965 Poznań, Poland
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| Abstract |
We consider the~operators $L_{m,n}^{\{i\}}$ of the~Szasz-Mirakjan type in some weighted
spaces of continuous functions of two variables. For these operators we give
theorems of degree of approximation, the~Voronovkaya type theorem,
the~Bernstein type inequality and theorem on convergence of partial
derivatives of $L_{m,n}^{\{i\}}(f;\cdot,\cdot)$.
These theorems are some analogues of the~results given in [3]--[8].
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| Keywords |
Szasz-Mirakjan operators, weighted spaces of continuous functions, two variables, degree of approximation, Voronovskaya theorem, Bernstein type inequality
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| DOI |
doi:10.30970/ms.10.1.3-16
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Reference |
1. . M. Becker Global approximation theorems for Szasz-Mirakjan and Baskakov operators in polynomial weight spaces // Indian Univ. Math. J.V.27№1–1978p.127–142
2. M. Becker, D. Kucharski, R.J. Nessel Global approximation theorems for Szasz-Mirakjan operators in exponential weight spacesLinear Spaces and Approximation (Proc. Conf. Oberwolfach, 1977) , Birkhäuser Verlag, Basel, ISNMV.40–1978p.319–333 3. B. Firlej, L. Rempulska Approximation of functions by some operators of the Szasz-Mirakjan type// Fasc. Math.V.27p.17–27–1997 4. M. Leśniewicz, L. Rempulska Approximation by some operators of the Szasz-Mirakjan type in exponential weight spaces// Glasnik MatematickiV.32№52–1997p.57–69 5. L. Rempulska, M. Skorupka Approximation of functions by some operators of the Szasz-Mirakjan type// Fasc. Math.V.26p.125–137–1996 6. L. Rempulska, M. Skorupka Approximation theorems for some operators of the Szasz-Mirakjan type in exponential weight spaces// Publicacije Elektroteh. Fak. (Beograd), Ser. Mat.V.7–1996p.9–18 7. L. Rempulska, M. Skorupka The Voronovskaya theorem for some operators of the Szasz-Mirakjan type // Le MatematicheV.50№2–1995p.251–261 8. L. Rempulska, M. Skorupka The Bershtein inequality for some operators of the Szasz-Mirakjan type // Note di Matematica V.14№2–1994p. 277-290 9. V. Totik Uniform approximation by Szasz-Mirakjan type operators // Acta Math. Hung. V.41–1983№3–4p.291–307 |
| Pages |
3-16
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| Volume |
10
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| Issue |
1
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| Year |
1998
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| Journal |
Matematychni Studii
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| Full text of paper | |
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