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Better Error Estimation for a Certain Family of Summation Integral Type Operators

Year 2012, Volume 25, Issue 1, 97 - 106, 24.01.2012

Abstract

In the present paper, we propose a modification for a certain family of summation integral type operators. We study direct results on the modified operators. It is also observed that our modified operators have better estimates over the original operators.

Key words and phrases: Better error estimation, Peetre.s functional, Lipschitz condition, Bézier variant, Bounded variation function.

 

References

  • DeVore R.A., Lorentz G. G., Constructive Approximation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 303 Springer-Verlag, Berlin, 1993.
  • Duman O.,Ozarslan M. A., Della Vecchia B., Modi.ed Szász- Mirakjan-Kantorovich operators preserving linear functions, Turkish. J. Math., 33 , no. 2, 151-158, (2009).
  • Gupta V., Gupta M. K., Vasishtha V., Simultaneous approximations by summation integral type operators, Nonlinear Funct. Anal. and Appl., 8(3), 399-412, (2003).
  • Gupta V., Ivan M., Rate of simultaneous approximation for the Bézier variant of certain operators, Appl. Math. Comput., 199 , no. 1, 392.395, (2008).
  • Ispir N.and Yuksel I, On the Bézier variant of Srivastava-Gupta operators, Appl. Math. E-Notes, 5 , 129-137, (2005).
  • May C. P., On Phillips operators, J. Approximation Theory, 20(4), 315-332, (1977).
  • Phillips R. S., An inversion formula for Laplace transforms and semi-groups of linear operators, Ann. of Math., 59 (2) , 352-356, (1954).
  • Srivastava H. M., Gupta V., A certain family of summation integral type operators, Math. Comput. Modelling, 37 (12-13) , 1307-1315, (2003).
  • Yuksel I., Ispir N., Weighted approximation by a certain family of summation integral-type operators, Comput. Math. Appl., 52 , no. 10-11, 1463. 1470, (2006).

Year 2012, Volume 25, Issue 1, 97 - 106, 24.01.2012

Abstract

References

  • DeVore R.A., Lorentz G. G., Constructive Approximation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 303 Springer-Verlag, Berlin, 1993.
  • Duman O.,Ozarslan M. A., Della Vecchia B., Modi.ed Szász- Mirakjan-Kantorovich operators preserving linear functions, Turkish. J. Math., 33 , no. 2, 151-158, (2009).
  • Gupta V., Gupta M. K., Vasishtha V., Simultaneous approximations by summation integral type operators, Nonlinear Funct. Anal. and Appl., 8(3), 399-412, (2003).
  • Gupta V., Ivan M., Rate of simultaneous approximation for the Bézier variant of certain operators, Appl. Math. Comput., 199 , no. 1, 392.395, (2008).
  • Ispir N.and Yuksel I, On the Bézier variant of Srivastava-Gupta operators, Appl. Math. E-Notes, 5 , 129-137, (2005).
  • May C. P., On Phillips operators, J. Approximation Theory, 20(4), 315-332, (1977).
  • Phillips R. S., An inversion formula for Laplace transforms and semi-groups of linear operators, Ann. of Math., 59 (2) , 352-356, (1954).
  • Srivastava H. M., Gupta V., A certain family of summation integral type operators, Math. Comput. Modelling, 37 (12-13) , 1307-1315, (2003).
  • Yuksel I., Ispir N., Weighted approximation by a certain family of summation integral-type operators, Comput. Math. Appl., 52 , no. 10-11, 1463. 1470, (2006).

Details

Primary Language English
Journal Section Mathematics
Authors

İsmet YUKSEL>

Publication Date January 24, 2012
Published in Issue Year 2012, Volume 25, Issue 1

Cite

Bibtex @ { gujs97381, journal = {Gazi University Journal of Science}, eissn = {2147-1762}, address = {}, publisher = {Gazi University}, year = {2012}, volume = {25}, number = {1}, pages = {97 - 106}, title = {Better Error Estimation for a Certain Family of Summation Integral Type Operators}, key = {cite}, author = {Yuksel, İsmet} }
APA Yuksel, İ. (2012). Better Error Estimation for a Certain Family of Summation Integral Type Operators . Gazi University Journal of Science , 25 (1) , 97-106 . Retrieved from https://dergipark.org.tr/en/pub/gujs/issue/7422/97381
MLA Yuksel, İ. "Better Error Estimation for a Certain Family of Summation Integral Type Operators" . Gazi University Journal of Science 25 (2012 ): 97-106 <https://dergipark.org.tr/en/pub/gujs/issue/7422/97381>
Chicago Yuksel, İ. "Better Error Estimation for a Certain Family of Summation Integral Type Operators". Gazi University Journal of Science 25 (2012 ): 97-106
RIS TY - JOUR T1 - Better Error Estimation for a Certain Family of Summation Integral Type Operators AU - İsmetYuksel Y1 - 2012 PY - 2012 N1 - DO - T2 - Gazi University Journal of Science JF - Journal JO - JOR SP - 97 EP - 106 VL - 25 IS - 1 SN - -2147-1762 M3 - UR - Y2 - 2023 ER -
EndNote %0 Gazi University Journal of Science Better Error Estimation for a Certain Family of Summation Integral Type Operators %A İsmet Yuksel %T Better Error Estimation for a Certain Family of Summation Integral Type Operators %D 2012 %J Gazi University Journal of Science %P -2147-1762 %V 25 %N 1 %R %U
ISNAD Yuksel, İsmet . "Better Error Estimation for a Certain Family of Summation Integral Type Operators". Gazi University Journal of Science 25 / 1 (January 2012): 97-106 .
AMA Yuksel İ. Better Error Estimation for a Certain Family of Summation Integral Type Operators. Gazi University Journal of Science. 2012; 25(1): 97-106.
Vancouver Yuksel İ. Better Error Estimation for a Certain Family of Summation Integral Type Operators. Gazi University Journal of Science. 2012; 25(1): 97-106.
IEEE İ. Yuksel , "Better Error Estimation for a Certain Family of Summation Integral Type Operators", Gazi University Journal of Science, vol. 25, no. 1, pp. 97-106, Jan. 2012