Approximation by Matrix Transforms in Weighted Lebesgue Spaces with Variable Exponent

Approximation by Nörlund and Riesz means in weighted Lebesgue space with variable exponent

“…After that Guven extended this results to triangular matrix transforms in [16]. In weighted Lebesgue space with variable exponent Isra…lov and Testici were investigated the approximation properties of matrix transform of Fourier series in [18]. In the Lebesgue space with variable exponent approximation Nörlund and Riesz submethods were studied in [20].…”

“…2 A p( ) ; the direct and inverse theorems of approximation theory in the weighted Lebesgue space with variable exponent were proved in [18] and [19], respectively. For the formulations of the results obtained in this work we need some auxiliary results proved in [18,19]. Thus, consecutively r times, using this inequality, we have…”

Approximation by matrix transforms in weighted Orlicz spaces

“…= n k=0 p k . As in [26] we define Nörlund means of the Fourier series of f with respect to the sequence {p n } the following form:…”

“…In particular, a constructive characterization of the generalized Lipschitz classes in these spaces was obtained in [24]. Approximation properties of the matrix transforms of functions in the weighted variable exponent Lebesgue spaces were investigated in [26]. In this work using modulus of continuity in weighted Orlicz spaces we define Lipschitz class Lip(α, M, ω).…”

Multiplier and approximation theorems in Smirnov classes with variable exponent

“…Detailed information about these investigations can be found in [4,5,[11][12][13]22,30] and the references given therein. In the variable exponent Smirnov classes some approximation problems were also investigated in [14,16,18].…”