Abstract
In the present article some inequalities of trigonometric approximation are proved in Orlicz spaces generated by a quasiconvex Young function. Also, the main one-sided approximation problems are investigated.
Keywords
Fractional moduli of smoothness Direct theorem Converse theorem Fractional derivative One-sided approximation
References
- Akg¨un, R. Approximating polynomials for functions of weighted Smirnov-Orlicz spaces, J. Funct. Spaces Appl., to appear.
- Akg¨un R. and Israfilov D. M. Simultaneous and converse approximation theorems in weighted Orlicz space, Bull. Belg. Math. Soc. Simon Stevin 17, 13–28, 2010.
- Akg¨un R. and Israfilov D. M. Approximation in weighted Orlicz spaces, Math. Slovaca, to appear.
- Doronin V. G. and Ligun A. A. Best one-sided approximation of the classes WrV(r > −1) by trigonometric polynomials in the Lmetric, Mat. Zametki 22 (3) (in Russian), 357–370, 1977.
- Israfilov D. M. and Guven A. Approximation by trigonometric polynomials in weighted Orlicz spaces, Studia Math. 174 (2), 147–168, 2006.
- Samko S. G., Kilbas A. A. and Marichev O. I. Fractional Integrals and Derivatives, Theory and Applications(Gordon and Breach Science Publishers, Yverdon, 1993).
- Zygmund A. Trigonometric Series (Cambridge University Press, New York, 1959).
Abstract
References
- Akg¨un, R. Approximating polynomials for functions of weighted Smirnov-Orlicz spaces, J. Funct. Spaces Appl., to appear.
- Akg¨un R. and Israfilov D. M. Simultaneous and converse approximation theorems in weighted Orlicz space, Bull. Belg. Math. Soc. Simon Stevin 17, 13–28, 2010.
- Akg¨un R. and Israfilov D. M. Approximation in weighted Orlicz spaces, Math. Slovaca, to appear.
- Doronin V. G. and Ligun A. A. Best one-sided approximation of the classes WrV(r > −1) by trigonometric polynomials in the Lmetric, Mat. Zametki 22 (3) (in Russian), 357–370, 1977.
- Israfilov D. M. and Guven A. Approximation by trigonometric polynomials in weighted Orlicz spaces, Studia Math. 174 (2), 147–168, 2006.
- Samko S. G., Kilbas A. A. and Marichev O. I. Fractional Integrals and Derivatives, Theory and Applications(Gordon and Breach Science Publishers, Yverdon, 1993).
- Zygmund A. Trigonometric Series (Cambridge University Press, New York, 1959).
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | February 1, 2011 |
| Published in Issue | Year 2011 Volume: 40 Issue: 2 |