Communications of the
Korean Mathematical Society CKMS

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.