APPROXIMATING CLASSES OF FUNCTIONS DEFINED BY A GENERALISED MODULUS OF SMOOTHNESS

Yıl 2013, Cilt: 1 Sayı: 2, 84 - 89, 01.12.2013

Faton M. Berısha Nimete Sh.berısha

Öz

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

Anahtar Kelimeler

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

Kaynakça

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• 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: [e-mail] N. Sh. Berisha, Faculty of Mathematics and Sciences, University of Prishtina, N¨ena
• Terez¨e 5, 10000 Prishtin¨e, Kosovo E-mail address: [e-mail]