Glasnik Matematicki, Vol. 43, No.1 (2008), 121-136.

APPROXIMATION AND MODULI OF FRACTIONAL ORDERS IN SMIRNOV-ORLICZ CLASSES

Ramazan Akgün and Daniyal M. Israfilov

Balikesir University, Faculty of Science and Art, Department of Mathematics, 10145, Balikesir, Turkey
e-mail: rakgun@balikesir.edu.tr

Institute of Math. and Mech. NAS Azerbaijan, F. Agayev Str. 9, Baku, Azerbaijan
e-mail: mdaniyal@balikesir.edu.tr

Abstract.   In this work we investigate the approximation problems in the Smirnov-Orlicz spaces in terms of the fractional modulus of smoothness. We prove the direct and inverse theorems in these spaces and obtain a constructive descriptions of the Lipschitz classes of functions defined by the fractional order modulus of smoothness, in particular.

2000 Mathematics Subject Classification.   30E10, 46E30, 41A10, 41A25.

Key words and phrases.   Orlicz space, Smirnov-Orlicz class, Dini-smooth curve, direct theorems, inverse theorems, fractional modulus of smoothness.

Full text (PDF) (free access)

DOI: 10.3336/gm.43.1.09

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