Communications of the
Korean Mathematical Society

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



Commun. Korean Math. Soc. 2023; 38(1): 163-178

Online first article December 7, 2022      Printed January 31, 2023

Copyright © The Korean Mathematical Society.

Functions subordinate to the exponential function

Priya G. Krishnan, Vaithiyanathan Ravichandran, Ponnaiah Saikrishnan

National Institute of Technology; National Institute of Technology; National Institute of Technology


We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function $p$ defined on the unit disc so that the function $p$ is subordinate to the function $e^z$. These results are applied to find sufficient conditions for the normalised analytic functions $f$ defined on the unit disc to satisfy the subordination $zf'(z)/f(z) \prec e^z$.

Keywords: Univalent functions, starlike functions, convex functions, close-to-convex functions, exponential function, differential subordination

MSC numbers: 30C80, 30C45

Supported by: The first author is supported by Junior Research Fellowship from University Grants Commission, New Delhi.