Article
Kyungpook Mathematical Journal 2018; 58(2): 257-270
Published online June 23, 2018
Copyright © Kyungpook Mathematical Journal.
First Order Differential Subordinations for Carathéodory Functions
Shweta Gandhi, Sushil Kumar and V. Ravichandran*
Department of Mathematics, University of Delhi, Delhi–110007, India, e-mail : gandhishwetagandhi@gmail.com, Bharati Vidyapeeth’s College of Engineering, Delhi–110063, India, e-mail : sushilkumar16n@gmail.com, Department of Mathematics, University of Delhi, Delhi–110007, India, e-mail : vravi@maths.du.ac.in; vravi68@gmail.com
Received: April 19, 2017; Accepted: September 9, 2017
The well-known theory of differential subordination developed by Miller and Mocanu is applied to obtain several inclusions between Carathéodory functions and starlike functions. These inclusions provide sufficient conditions for normalized analytic functions to belong to certain class of Ma-Minda starlike functions.
Keywords: Differential subordination, starlike function, Carathé,odory functions, Janowski function