@article{Cakir_Aykol_Guliyev_Serbetci_2021, title={Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces}, volume={13}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/4798}, DOI={10.15330/cmp.13.3.750-763}, abstractNote={<p>In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\mathcal{M }_{p(\cdot),\lambda(\cdot)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(\cdot)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\mathcal{M }_{p(\cdot),\lambda(\cdot)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\mathcal{\widetilde{M }_{p(\cdot),\lambda(\cdot)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\mathcal{M }_{p(\cdot),\lambda(\cdot)}(I_{0},w)$.</p>}, number={3}, journal={Carpathian Mathematical Publications}, author={Cakir, Z. and Aykol, C. and Guliyev, V.S. and Serbetci, A.}, year={2021}, month={Dec.}, pages={750–763} }