Convergence of Szász-Mirakyan type operators

Authors

  • Zbigniew Walczak Poznan University of Technology, Poznan, Poland

DOI:

https://doi.org/10.33993/jnaat361-860

Keywords:

Szász-Mirakyan operator, polynomial weighted spaces, order of approximation
Abstract views: 244

Abstract

We introduce certain modifications of Szász-Mirakyan operators and we study approximation properties of these operators. The result is in a form convenient for applications.

Downloads

Download data is not yet available.

References

Becker, M., Global approximation theorems for Szasz--Mirakyan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J., 27(1), pp. 127-142, 1978, https://doi.org/10.1512/iumj.1978.27.27011 DOI: https://doi.org/10.1512/iumj.1978.27.27011

Becker, M., Kucharski, D. and Nessel, R. J., Global approximation theorems for the Szasz-Mirakjan operators in exponential weight spaces, Linear Spaces and Approximation (Proc. Conf. Oberwolfach, 1977), Birkhäuser Verlag, Basel ISNM, 40, pp. 319-333, 1978, https://doi.org/10.1007/978-3-0348-7180-8_28 DOI: https://doi.org/10.1007/978-3-0348-7180-8_28

Ciupa, A., Approximation by a generalized Szasz type operators, J. Comput. Anal. Appl., 5(4), pp. 413-424, 2003, https://doi.org/10.1023/a:1024521315495 DOI: https://doi.org/10.1023/A:1024521315495

De Vore, R. A. and Lorentz, G. G., Constructive Approximation, Springer-Verlag, Berlin, 1993, https://doi.org/10.1007/978-3-662-02888-9 DOI: https://doi.org/10.1007/978-3-662-02888-9

Ditzian, Z. and Totik, V. Moduli of Smoothness, Springer-Verlag, New York 1987, https://doi.org/10.1007/978-1-4612-4778-4 DOI: https://doi.org/10.1007/978-1-4612-4778-4

Feng, G., Weighted approximation on Szasz-type operators, Anal. Theory Appl., 19(1), pp. 47-54, 2003, https://doi.org/10.1007/bf02835477 DOI: https://doi.org/10.1007/BF02835477

Feng, G., A characterization of pointwise approximation for linear combinations of Szász-type operators, Chinese Quart. J. Math., 19(4), pp. 379-384, 2004.

Gupta, P. and Gupta, V., Rate of convergence on Baskakov-Szasz type operators, Fasc. Math., 31, pp. 37-44, 2001.

Gupta, V., An estimate on the convergence of Baskakov-Bézier operators, J. Math. Anal. Appl., 312(1), pp. 280-288, 2005, https://doi.org/10.1016/j.jmaa.2005.03.041 DOI: https://doi.org/10.1016/j.jmaa.2005.03.041

Gupta, V. and Maheshwari, P., On Baskakov-Szasz type operators, Kyungpook Math. J., 43(3), pp. 315-325, 2003.

Gupta, V. and Pant, R.P., Rate of convergence of the modified Szasz-Mirakyan operators on functions of bounded variation, J. Math. Anal. Appl., 233(2), pp. 476-483, 1999, https://doi.org/10.1006/jmaa.1999.6289 DOI: https://doi.org/10.1006/jmaa.1999.6289

Gupta, V., Vasishtha, V. and Gupta, M.K. Rate of convergence of the Szasz-Kantorovitch-Bezier operators for bounded variation functions, Publ. Inst. Math. (Beograd)(N.S.), 72(86), pp. 137-143, 2002, https://doi.org/10.2298/pim0272137g DOI: https://doi.org/10.2298/PIM0272137G

Guo, S., Li, C., Sun, Y., Yand, G. and Yue, S., Pointwise estimate for Szasz-type operators, J. Approx. Th., 94, pp. 160-171, 1998, https://doi.org/10.1006/jath.1998.3200 DOI: https://doi.org/10.1006/jath.1998.3200

Grof, J., Über Approximation durch Polynome mit Belegfunktionen, Acta Math. Acad. Sci. Hungar., 35, pp. 109-116, 1980, https://doi.org/10.1007/bf01896829 DOI: https://doi.org/10.1007/BF01896829

Ispir, N. and Atakut, C., Approximation by modified Szasz-Mirakyan operators on weighted spaces, Proc. Indian acad. Sci. Math. Sci., 112(4), pp. 571-578, 2002, https://doi.org/10.1007/bf02829690 DOI: https://doi.org/10.1007/BF02829690

Lehnhoff, H.G., On a Modified Szasz-Mirakjan Operator, J. Approx. Th., 42, pp. 278-282, 1984, https://doi.org/10.1016/0021-9045(84)90045-5 DOI: https://doi.org/10.1016/0021-9045(84)90045-5

Rempulska, L. and Walczak, Z., Modified Szasz-Mirakyan operators, Mat. Balcanica (New Ser.), 18(1-2), pp. 53-63, 2004.

Totik, V., Uniform approximation by Szasz-Mirakyan type operators, Acta Math. Hung., 41(3-4), pp. 291-307, 1983, https://doi.org/10.1007/bf01961317 DOI: https://doi.org/10.1007/BF01961317

Walczak, Z., On certain positive linear operators in weighted polynomial spaces, Acta Math. Hungar., 1013, pp. 179-191, 2003, https://doi.org/10.1023/b:amhu.0000003902.41088.ce DOI: https://doi.org/10.1023/B:AMHU.0000003902.41088.ce

Walczak, Z., On the rate of convergence for modified Szasz-Mirakyan operators, Analele Universităţii din Timişoara, 61(2), pp. 141-149, 2003.

Walczak, Z., Approximation by some linear positive operators in polynomial weighted spaces, Publ. Math. Debrecen, 64 (3-4), pp. 353-367, 2004. DOI: https://doi.org/10.5486/PMD.2004.2892

Walczak, Z., On the rate of convergence for some linear operators, Hiroshima Math. J., 35(1), pp. 115-124, 2005, https://doi.org/10.32917/hmj/1150922488 DOI: https://doi.org/10.32917/hmj/1150922488

Xiehua, S., On the convergence of the modified Szasz-Mirakjan operator, Approx. Theory Appl., 10(1), pp. 20-25, 1994, https://doi.org/10.1007/BF02836295. DOI: https://doi.org/10.1007/BF02836295

Downloads

Published

2007-02-01

How to Cite

Walczak, Z. (2007). Convergence of Szász-Mirakyan type operators. Rev. Anal. Numér. Théor. Approx., 36(1), 107–113. https://doi.org/10.33993/jnaat361-860

Issue

Section

Articles