Abstract
UDC 517.5 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 and spirallike functions of type with the complex order We obtain sharp estimates for the coefficient of the second term in the Taylor series of functions belonging to the mentioned classes. In the main part of this paper, we obtain the necessary and sufficient conditions of boundedness for the image of the open unit disk 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. Finally, we obtain an estimate of the Schwartzian norm of the above operators in these spaces.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.