Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024



Commun. Korean Math. Soc. 2022; 37(4): 995-1007

Online first article September 21, 2022      Printed October 31, 2022

Copyright © The Korean Mathematical Society.

Properties of functions with bounded rotation associated with lima\c{c}on class

Kanwal Jabeen, Afis Saliu

Punjab College; Gombe State University


In this article, we initiate subclasses of functions with boundary and radius rotations that are related to lima\c{c}on domains and examine some of their geometric properties. Radius results associated with functions in these classes and their linear combination are studied. Furthermore, the growth rate of coefficients, arc length and coefficient estimates are derived for these novel classes. Overall, some useful consequences of our findings are also illustrated.

Keywords: Univalent functions, Schwarz functions, lima\c{c}on domains, subordination, analytic functions, functions with bounded boundary and radius rotations

MSC numbers: Primary 30C45, 30C50

Supported by: The second author would like to thank Mr. Muhammad Akram(Director of Punjab Group of Colleges, Rwp/Isb) and Mr. Babar Bashir (Evening Incharge, Punjab College, Ayub Park Campus, Rwp), Pakistan, for their active role in her academic development and providing excellent research and academic environment.