@article{Akgün_2023, title={A modulus of smoothness for some Banach function spaces}, volume={75}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/970}, DOI={10.3842/umzh.v75i8.970}, abstractNote={<p class="p1">UDC 517.5</p> <p class="p1">Based on the Steklov operator, we consider a modulus of smoothness of functions in some Banach function spaces, which can be not translation invariant and establish its main properties. A constructive characterization of the Lipschitz class is obtained by using the Jackson-type direct theorem and inverse theorem of trigonometric approximation. As application, we present several examples of related (weighted) function spaces.</p>}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Akgün, Ramazan}, year={2023}, month={Aug.}, pages={1015 - 1031} }