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.
Keywords
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).
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 | |
| Publication Date | January 24, 2012 |
| Published in Issue | Year 2012 Volume: 25 Issue: 1 |