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- Title
Volterra-Type Operators on the Subclasses of Univalent Functions.
- Authors
Mahboobi, M.
- Abstract
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.
- Subjects
STAR-like functions; COMPOSITION operators; UNIVALENT functions; CONVEX functions; FUNCTION spaces
- Publication
Ukrainian Mathematical Journal, 2022, Vol 74, Issue 1, p87
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-022-02049-7