On <i>q</i>-Starlike Functions Defined by <i>q</i>-Ruscheweyh Differential Operator in Symmetric Conic Domain

Abstract

Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to first define and then study a new class of holomorphic functions using the q-Ruscheweyh differential operator. A new class k−STqτC,D of k-Janowski starlike functions associated with the symmetric conic domain, which are defined by the generalized Ruscheweyh derivative operator in the open unit disk, is introduced. The necessary and sufficient condition for a function to be in the class k−STqτC,D is established. In addition, the coefficient bound, partial sums and radii of starlikeness for the functions from the class of k-Janowski starlike functions related with symmetric conic domain are included.

Keywords

• holomorphic functions
• starlike functions
• <i>q</i>-starlike functions
• Ruscheweyh <i>q</i>-differential operator
• symmetric conic domain