q-Analog of Prestarlike Functions

Abstract

We introduce a class Rαq of q-prestarlike functions of order α by using q-difference operator. We obtain necessary and sufficient conditions involving convolution for functions to be in the class Rαq. We prove that the well-known class of analytic prestarlike functions, Rα, is properly contained in Rαq. Apart from finding bounds on some initial coefficients of functions in the class Rαq, we also investigate some convolution properties of functions in the class Rαq. The results of the present manuscript essentially generalize some well-known results in the literature. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.