Volterra-Type Operators on the Subclasses of Univalent Functions

We examine necessary and sufficient conditions for a member to belong to the class of starlike and convex functions of complex order b  ( b  ≠ 0) and spirallike functions of type λ − π 2 < λ < π 2 order b  ( b  ≠ 0) . We obtain sharp estimates for the coefficient of the second term in the Tayl...

Full description

Saved in:
Bibliographic Details
Published in:Ukrainian mathematical journal 2022-06, Vol.74 (1), p.87-101
Main Author: Mahboobi, M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Operators
Statistics
Taylor series
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We examine necessary and sufficient conditions for a member to belong to the class of starlike and convex functions of complex order b  ( b  ≠ 0) and spirallike functions of type λ − π 2 < λ < π 2 order b  ( b  ≠ 0) . We obtain sharp estimates for the coefficient of the second term in the Taylor series of functions that belong to the indicated classes. In the main part of the paper, we obtain necessary and sufficient conditions of boundedness for the image of the open unit disk D z ∈ ℂ : z < 1 under the action of a Volterra-type operator and the product of a composition operator and a Volterra-type operator in the space of univalent functions and its subspace. Finally, we obtain an estimate for the Schwartzian norm of the above operators in these spaces.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-022-02049-7