TY  - JOUR
T1  - APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS
AU  - Berısha, Faton M.
AU  - Sh.berısha, Nimete
PY  - 2013
DA  - December
JF  - Mathematical Sciences and Applications E-Notes
JO  - Math. Sci. Appl. E-Notes
PB  - Murat TOSUN
WT  - DergiPark
SN  - 2147-6268
SP  - 84
EP  - 89
VL  - 1
IS  - 2
LA  - en
AB  - 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
KW  - generalised Lipschitz classes
KW  - generalised modulus of smoothness
KW  - asymmetric generalised shift operator
KW  - theorem of coincidence of classes
CR  - 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.
CR  - 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.
CR  - 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.
CR  - 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.
CR  - 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
CR  - 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
CR  - Terez¨e 5, 10000 Prishtin¨e, Kosovo E-mail address: nimete.berisha@gmail.com
UR  - https://dergipark.org.tr/en/pub/mathenot/article/207648
L1  - https://dergipark.org.tr/en/download/article-file/182481
ER  -