Distortion, Radius of Concavity and Several Other Radii Results for Certain Classes of Functions

• Published in: Computational methods and function theory Vol. 25; no. 2; pp. 393 - 418
• Main Authors: Bhowmik, Bappaditya, Biswas, Souvik
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.06.2025
• Subjects: Concavity; Convexity
• ISSN: 1617-9447; 2195-3724
• DOI: 10.1007/s40315-024-00525-8

Let S(p) be the class of all meromorphic univalent functions defined in the unit disc D of the complex plane with a simple pole at z=p and normalized by the conditions f(0)=0 and f′(0)=1. In this article, we establish an estimate of the quantity |zf′/f| and obtain the region of variability of the function zf′′/f′ for z∈D, f∈S(p). After that, we define radius of concavity and compute the same for functions in S(p) and for some other well-known classes of functions. We also explore linear combinations of functions belonging to S(p) and some other classes of analytic univalent functions and investigate their radii of univalence, convexity and concavity.