@article{Vakarchuk_Vakarchuk_2022, title={$K$-functionals and extreme problems of the theory of approximation for classes of analytic functions in the circle. I}, volume={74}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6980}, DOI={10.37863/umzh.v74i4.6980}, abstractNote={<p>УДК 517.5</p> <p>Based on the Hadamard composition in the Hardy, Bergman and Gvaradze Banach spaces of functions analytic in the unit circle, we consider a generalization of the $K$-functional.<span class="Apple-converted-space"> </span>In solving some extreme problems of the theory of approximation in the complex plane, we obtain certain exact results in the case where the indicated $K$-functional is used as a<span class="Apple-converted-space"> </span>characteristic of smoothness.<span class="Apple-converted-space"> </span></p>}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={VakarchukS. B. and VakarchukM. B.}, year={2022}, month={May}, pages={469 - 485} }