Research Article

Estimates for the Pre-Schwarzian norm for certain subclasses of analytic functions

Published in: Quaestiones Mathematicae
Volume 49 , issue 3 , 2026 , pages: 371–385

DOI: 10.2989/16073606.2025.2589840

Author(s): Rashid Ali Government College University Faisalabad, Pakistan , Mohsan Raza Government College University Faisalabad, Pakistan

Keywords: 30C45 , 30C50 , 30C80 , Starlike functions , convex functions , subordination , limacon , generalized telephone numbers , pre-Schwarzian norm

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Abstract

For λ ≥ 1, let be the class of analytic functions f in the open unit disc defined by . Similarly, for the class is defined by . In this article, we present estimates for the pre-Schwarzian norm of functions in the classes and , as well as for the pre-Schwarzian norm of the Alexander transformation of functions in the same classes. Most of the results presented in this article are sharp.

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