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Linear Methods Of Summing Fourier Series And Approximation In Weighted Orliczspaces, Sadulla Jafarov
Linear Methods Of Summing Fourier Series And Approximation In Weighted Orliczspaces, Sadulla Jafarov
Turkish Journal of Mathematics
In the present work, we investigate estimates of the deviations of the periodic functions from the linear operators constructed on the basis of its Fourier series in reflexive weighted Orlicz spaces with Muckenhoupt weights. In particular, the orders of approximation of Zygmund and Abel-Poisson means of Fourier trigonometric series were estimated by the $k-th$~modulus of smoothness in reflexive weighted Orlicz spaces with Muckenhoupt weights.
Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$, Ahmet Hamdi̇ Avşar, Hüseyi̇n Koç
Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$, Ahmet Hamdi̇ Avşar, Hüseyi̇n Koç
Turkish Journal of Mathematics
In this paper, we study Jackson and Stechkin type theorems of trigonometric polynomial approximation in the space $A_{w,\vartheta }^{p,q(\cdot )}$ by considering a modulus of smoothness defined by virtue of the Steklov operator.
Gadjieva's Conjecture, $K$-Functionals, And Someapplications In Weighted Lebesgue Spaces, Ramazan Akgün
Gadjieva's Conjecture, $K$-Functionals, And Someapplications In Weighted Lebesgue Spaces, Ramazan Akgün
Turkish Journal of Mathematics
We prove that Gadjieva's conjecture holds true as stated in her PhD thesis. The positive solution of this conjecture allows us to obtain improved versions of the Jackson--Stechkin type inequalities obtained in her thesis and some others. As an application, an equivalence of the modulus of smoothness with the realization functional is established. We obtain a characterization class for the modulus of smoothness.