@article{Mahboobi_2022, title={Volterra-type operator on the subclasses of univalent functions}, volume={74}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/1116}, DOI={10.37863/umzh.v74i1.1116}, abstractNote={<p>UDC 517.5</p> <p>In this article, we examine the necessary and sufficient conditions for a member to belong to the class of starlike and convex functions of complex order $b$ $(b
eq 0)$ and spirallike functions of type $ \lambda$ $\Big( {-\dfrac{\pi}{2 }<\lambda<\dfrac{\pi}{2} \Big)$ with the complex order $b$ $(b
eq 0).$ <br>We obtain sharp estimates for the coefficient of the second term in the Taylor series of functions belonging to the mentioned classes.</p> <p>In the main part of this paper, we obtain the necessary and sufficient conditions of boundedness for the image of the open unit disk $ \mathbb{D}=\lbrace z\in \mathbb{C}:\vert z\vert<1\rbrace $ under the action of a Volterra-type operator and the product of the composition operator and Volterra-type operator in the space of univalent functions and its subspace. <br>Finally, we obtain an estimate of the Schwartzian norm of the above operators in these spaces.</p>}, number={1}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Mahboobi, M.}, year={2022}, month={Jan.}, pages={77 - 88} }