APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS

Faton M. Berısha; Nimete Sh.berısha

EN

APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS

Abstract

In the present paper, we use a generalised shift operator in order to define a generalised modulus of smoothness. By its means, we definegeneralised Lipschitz classes of functions, and we give their constructive characteristics. Specifically, we prove certain direct and inverse types theorems inapproximation theory for best approximation by algebraic polynomials

Keywords

generalised Lipschitz classes, generalised modulus of smoothness,asymmetric generalised shift operator, theorem of coincidence of classes

References

F. M. Berisha. On coincidence of classes of functions defined by a generalized modulus of smoothness and the appropriate inverse theorem. Math. Montisnigri, 9:15–36, 1998.
N. Sh. Berisha and F. M. Berisha. Approximating classes of functions defined by operators of differentiation or operators of generalised translation by means of algebraic polynomials. Int. J. Math. Anal. (Ruse), 6(55):2709–2729, 2012.
M. K. Potapov and F. M. Berisha. Approximation of classes of functions defined by a gener- alized k-th modulus of smoothness. East J. Approx., 4(2):217–241, 1998.
M. K. Potapov and F. M. Berisha. Direct and inverse theorems of approximation theory for a generalized modulus of smoothness. Anal. Math., 25(3):187–203, 1999.
M. K. Potapov and F. M. Berisha. O svyazi mezhdu r-im obobshchennym medulem gladkosti i nailuchshimi priblizheniyami algebraicheskimi mnogochlenami. Fundam. Prikl. Mat., 5(2):563– 587, 1999. F. M. Berisha, Faculty of Mathematics and Sciences, University of Prishtina, N¨ena
Terez¨e 5, 10000 Prishtin¨e, Kosovo E-mail address: faton.berisha@uni-pr.edu N. Sh. Berisha, Faculty of Mathematics and Sciences, University of Prishtina, N¨ena
Terez¨e 5, 10000 Prishtin¨e, Kosovo E-mail address: nimete.berisha@gmail.com

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

Faton M. Berısha This is me

Nimete Sh.berısha This is me

Publication Date

December 1, 2013

Submission Date

March 9, 2015

Acceptance Date

-

Published in Issue

Year 2013 Volume: 1 Number: 2

IZ

https://izlik.org/JA86KC76JK

APA

Berısha, F. M., & Sh.berısha, N. (2013). APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS. Mathematical Sciences and Applications E-Notes, 1(2), 84-89. https://izlik.org/JA86KC76JK

AMA

1.Berısha FM, Sh.berısha N. APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS. Math. Sci. Appl. E-Notes. 2013;1(2):84-89. https://izlik.org/JA86KC76JK

Chicago

Berısha, Faton M., and Nimete Sh.berısha. 2013. “APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS”. Mathematical Sciences and Applications E-Notes 1 (2): 84-89. https://izlik.org/JA86KC76JK.

EndNote

Berısha FM, Sh.berısha N (December 1, 2013) APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS. Mathematical Sciences and Applications E-Notes 1 2 84–89.

IEEE

[1]F. M. Berısha and N. Sh.berısha, “APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS”, Math. Sci. Appl. E-Notes, vol. 1, no. 2, pp. 84–89, Dec. 2013, [Online]. Available: https://izlik.org/JA86KC76JK

ISNAD

Berısha, Faton M. - Sh.berısha, Nimete. “APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS”. Mathematical Sciences and Applications E-Notes 1/2 (December 1, 2013): 84-89. https://izlik.org/JA86KC76JK.

JAMA

1.Berısha FM, Sh.berısha N. APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS. Math. Sci. Appl. E-Notes. 2013;1:84–89.

MLA

Berısha, Faton M., and Nimete Sh.berısha. “APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS”. Mathematical Sciences and Applications E-Notes, vol. 1, no. 2, Dec. 2013, pp. 84-89, https://izlik.org/JA86KC76JK.

Vancouver

1.Faton M. Berısha, Nimete Sh.berısha. APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS. Math. Sci. Appl. E-Notes [Internet]. 2013 Dec. 1;1(2):84-9. Available from: https://izlik.org/JA86KC76JK