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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
https://izlik.org/JA63FY99CA

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
https://izlik.org/JA63FY99CA

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).
There are 9 citations in total.

Details

Primary Language English
Authors

İsmet Yuksel

Publication Date January 24, 2012
IZ https://izlik.org/JA63FY99CA
Published in Issue Year 2012 Volume: 25 Issue: 1

Cite

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. https://izlik.org/JA63FY99CA
AMA 1.Yuksel İ. Better Error Estimation for a Certain Family of Summation Integral Type Operators. Gazi University Journal of Science. 2012;25(1):97-106. https://izlik.org/JA63FY99CA
Chicago Yuksel, İsmet. 2012. “Better Error Estimation for a Certain Family of Summation Integral Type Operators”. Gazi University Journal of Science 25 (1): 97-106. https://izlik.org/JA63FY99CA.
EndNote Yuksel İ (January 1, 2012) Better Error Estimation for a Certain Family of Summation Integral Type Operators. Gazi University Journal of Science 25 1 97–106.
IEEE [1]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, [Online]. Available: https://izlik.org/JA63FY99CA
ISNAD Yuksel, İsmet. “Better Error Estimation for a Certain Family of Summation Integral Type Operators”. Gazi University Journal of Science 25/1 (January 1, 2012): 97-106. https://izlik.org/JA63FY99CA.
JAMA 1.Yuksel İ. Better Error Estimation for a Certain Family of Summation Integral Type Operators. Gazi University Journal of Science. 2012;25:97–106.
MLA Yuksel, İsmet. “Better Error Estimation for a Certain Family of Summation Integral Type Operators”. Gazi University Journal of Science, vol. 25, no. 1, Jan. 2012, pp. 97-106, https://izlik.org/JA63FY99CA.
Vancouver 1.İsmet Yuksel. Better Error Estimation for a Certain Family of Summation Integral Type Operators. Gazi University Journal of Science [Internet]. 2012 Jan. 1;25(1):97-106. Available from: https://izlik.org/JA63FY99CA