On the degrees of approximation of functions belonging to L^p (ω̃)_β class by matrix means of conjugate Fourier series

Slight extensions of some theorems on the rate of pointwise approximation of functions from some subclasses of <i>L^p</i>

“…Recently W. Lenski and B. Szal [5] considered the same deviation and additionally the deviations T n,A f (·) −f ·, π n+1 and T n,A (f ) − f in the case when the sequence {a n,k } is of Rest Bounded Variation or of Head Bounded Variation. Also some results of this type are obtained very recently in [1].…”

Degree of convergence of a function of several variables in generalized Hölder spaces

“…n,m∈Z 2 (−i sign m)C n,m (h)e i(nx+m𝑦) (w.r.t. variable 𝑦); (5) and ∑ ∑ n,m∈Z 2 (−i sign n)(−i sign m)C n,m (h)e i(nx+m𝑦) (w.r.t. both the variables x and 𝑦).…”

“…Degree of approximation of a function of one-dimensional variable in Lipschitz, Besov, Hölder, generalized Hölder spaces has been studied by the authors [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] using different single and product means of conjugate Fourier series. Different double summability means of double Fourier series and double conjugate Fourier series have been studied by the authors.…”