Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent

Abstract

We investigate the approximation properties of the trigonometric system in L p. / 2 : We consider the moduli of smoothness of fractional order and obtain direct and inverse approximation theorems together with a constructive characterization of a Lipschitz-type class.

Multiplier and approximation theorems in Smirnov classes with variable exponent

“…these theorems in the case of r=1 and p(·) ∈ P 0 ([0, 2π]) , using some other modulus of smoothness, were proved in [1][2][3]10,20,21]. For a wider class of the exponents p(·) , namely when…”

Derivatives of a polynomial of best approximation and modulus of smoothness in generalized Lebesgue spaces with variable exponent

“…In particular, some direct and inverse theorems in weighted and nonweighted Lebesgue spaces with variable exponent have been obtained in [9,10,16,21,[28][29][30]34].…”

Approximation by trigonometric polynomials of functions having (α, ψ)- derivatives in weighted variable exponent Lebesgue spaces

“…This allows us to consider approximation problems in L p(·) ω . Approximation by trigonometric polynomials in L p(·) ω was considered in [3]- [8] In [9,10], on the basis of the transformed Fourier series, the so-called lambda derivatives were introduced and inequalities are obtained in a refined form like the Besov and Timan inequalities.…”