On a class of Szász-Mirakyan type operators

Zbigniew Walczak

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 3, page 705-716
  • ISSN: 0011-4642

Abstract

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The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.

How to cite

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Walczak, Zbigniew. "On a class of Szász-Mirakyan type operators." Czechoslovak Mathematical Journal 58.3 (2008): 705-716. <http://eudml.org/doc/37862>.

@article{Walczak2008,
abstract = {The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.},
author = {Walczak, Zbigniew},
journal = {Czechoslovak Mathematical Journal},
keywords = {linear positive operator; polynomial weighted space; linear positive operator; polynomial weighted space},
language = {eng},
number = {3},
pages = {705-716},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a class of Szász-Mirakyan type operators},
url = {http://eudml.org/doc/37862},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Walczak, Zbigniew
TI - On a class of Szász-Mirakyan type operators
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 705
EP - 716
AB - The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.
LA - eng
KW - linear positive operator; polynomial weighted space; linear positive operator; polynomial weighted space
UR - http://eudml.org/doc/37862
ER -

References

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  1. Atakut, C., Ispir, N., The order of approximation by certain linear positive operators, Math. Balk., New Ser. 15 (2001), 25-33. (2001) Zbl1040.41007MR1882520
  2. Becker, M., 10.1512/iumj.1978.27.27011, Indiana Univ. Math. J. 27 (1978), 127-142. (1978) Zbl0358.41006MR0493079DOI10.1512/iumj.1978.27.27011
  3. Becker, M., Kucharski, D., Nessel, R. J., Global Approximation theorems for the Szasz-Mirakjan operators in exponential weight spaces. Linear Spaces and Approximation (Proc. Conf. Oberwolfach, 1977), ISNM, Int. Ser. Numer. Math. 40 (1978), 319-333. (1978) MR0499919
  4. Ciupa, A., On the approximation by Favard-Szasz type operators, Rev. Anal. Numér. Théor. Approx. 25 (1996), 57-61. (1996) Zbl0908.41010MR1607327
  5. Ciupa, A., Approximation by a generalized Szasz type operators, J. Comput. Anal. Appl. 5 (2003), 413-424. (2003) MR2000071
  6. Vore, R. A. De, Lorentz, G. G., Constructive Approximation, Springer Berlin (1993). (1993) MR1261635
  7. Feng, G., 10.1007/BF02835477, Anal. Theory Appl. 19 (2003), 47-54. (2003) Zbl1108.41301MR1996352DOI10.1007/BF02835477
  8. Feng, G., A characterization of pointwise approximation for linear combinations of Szász-type operators, Chinese Quart. J. Math. 19 (2004), 379-384. (2004) MR2131301
  9. Gupta, P., Gupta, V., Rate of convergence on Baskakov-Szasz type operators, Fasc. Math. 31 (2001), 37-44. (2001) MR1860546
  10. Gupta, V., 10.1016/j.jmaa.2005.05.017, J. Math. Anal. Appl. 313 (2006), 632-641. (2006) Zbl1092.41009MR2183324DOI10.1016/j.jmaa.2005.05.017
  11. Gupta, V., Maheshwari, P., On Baskakov-Szasz type operators, Kyungpook Math. J. 43 (2003), 315-325. (2003) Zbl1145.41307MR2003476
  12. Gupta, V., Pant, R. P., 10.1006/jmaa.1999.6289, J. Math. Anal. Appl. 233 (1999), 476-483. (1999) Zbl0931.41012MR1689649DOI10.1006/jmaa.1999.6289
  13. Gupta, V., Vasishtha, V., Gupta, M. K., 10.2298/PIM0272137G, Publ. Inst. Math., Nouv. Sér. 72 (2002), 137-143. (2002) Zbl1052.41005MR1997619DOI10.2298/PIM0272137G
  14. Guo, S., 10.1016/0021-9045(89)90114-7, J. Approximation Theory 56 (1989), 245-255. (1989) Zbl0677.41023MR0990339DOI10.1016/0021-9045(89)90114-7
  15. Guo, S., Li, C., Sun, Y., Yand, G., Yue, S., 10.1006/jath.1998.3200, J. Approximation Theory 94 (1998), 160-171. (1998) MR1637831DOI10.1006/jath.1998.3200
  16. Herzog, M., Approximation theorems for modified Szasz-Mirakjan operators in polynomial weight spaces, Matematiche 54 (1999), 77-90. (1999) Zbl0960.41015MR1776330
  17. Ispir, N., Weighted approximation by modified Favard-Szász operators, Int. Math. J. 3 (2003),1053-1060. (2003) MR2005685
  18. Ispir, N., Atakut, C., 10.1007/BF02829690, Proc. Indian Acad. Sci., Math. Sci. 112 (2002), 571-578. (2002) MR1941893DOI10.1007/BF02829690
  19. Lehnhoff, H. G., 10.1016/0021-9045(84)90045-5, J. Approximation Theory 42 (1984), 278-282. (1984) Zbl0573.41034MR0765443DOI10.1016/0021-9045(84)90045-5
  20. Lesniewicz, M., Rempulska, L., Approximation by some operators of the Szasz-Mirakjan type in exponential weight spaces, Glas. Mat., III. Ser. 32 (1997), 57-69. (1997) Zbl0880.41017MR1469620
  21. Li, S., 10.1006/jath.1996.3016, J. Approximation Theory 88 (1997), 139-153. (1997) Zbl0872.41008MR1429969DOI10.1006/jath.1996.3016
  22. Linsen, X., Xiaoping, Z., Pointwise characterization for combinations of Baskakov operators, Approximation Theory Appl. 18 (2002), 76-89. (2002) MR1928167
  23. Rempulska, L., Walczak, Z., On modified Baskakov operators, Proc. A. Razmadze Math. Inst. 133( (2003), 109-117. (2003) Zbl1042.41020MR2034442
  24. Rempulska, L., Walczak, Z., 10.1007/BF02835254, Anal. Theory Appl. 20 (2004), 1-15. (2004) Zbl1073.41021MR2574579DOI10.1007/BF02835254
  25. Rempulska, L., Walczak, Z., Modified Szasz-Mirakyan operators, Math. Balk., New Ser. 18 (2004), 53-63. (2004) Zbl1079.41022MR2076077
  26. Sahai, A., Prasard, G., 10.1016/0021-9045(85)90039-5, J. Approximation Theory 45 (1985), 122-128. (1985) MR0813006DOI10.1016/0021-9045(85)90039-5
  27. Totik, V., Uniform approximation by Szász-Mirakjan type operators, Acta Math. 41 (1983), 291-307. (1983) Zbl0513.41013MR0703742
  28. Walczak, Z., On certain linear positive operators in exponential weighted spaces, Math. J. Toyama Univ. 25 (2002), 109-118. (2002) Zbl1111.41017MR1963731
  29. Walczak, Z., On certain positive linear operators in weighted polynomial spaces, Acta Math. 101 (2003), 179-191. (2003) MR2018629
  30. Walczak, Z., Approximation properties of certain linear positive operators in exponential weighted spaces, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 42 (2003), 123-130. (2003) Zbl1054.41015MR2056027
  31. Walczak, Z., Approximation by some linear positive operators of functions of two variables, Saitama Math. J. 21 (2003), 23-31. (2003) Zbl1071.41023MR2068761
  32. Walczak, Z., On the rate of convergence for modified Baskakov operators, Liet. matem. rink 44 (2004), 124-130. (2004) Zbl1058.41007MR2116497
  33. Walczak, Z., Approximation by some linear positive operators in polynomial weighted spaces, Publ. Math. Debrecen 64 (2004), 353-367. (2004) Zbl1079.41023MR2058908
  34. Walczak, Z., Approximation properties of certain linear positive operators in polynomial weighted spaces of functions of one and two variables, Publ. Elektrotehn. Fak. Univ. Beograd 15 (2004), 52-65. (2004) Zbl1106.41020MR2104230
  35. Walczak, Z., On the convergence of the modified Szasz-Mirakyan operators, Yokohama Math. J. 51 (2004), 11-18. (2004) Zbl1063.41018MR2095839
  36. Walczak, Z., 10.32917/hmj/1150922488, Hiroshima Math. J. 35 (2005), 115-124. (2005) Zbl1079.41024MR2131378DOI10.32917/hmj/1150922488
  37. Wood, B., 10.1016/0021-9045(89)90132-9, J. Approximation Theory 56 (1989), 48-58. (1989) Zbl0677.41024MR0977873DOI10.1016/0021-9045(89)90132-9
  38. Xiehua, S., On the convergence of the modified Szasz-Mirakjan operator, Approximation Theory Appl. 10 (1994), 20-25. (1994) MR1287450

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