Convex Families of <i>q</i>-Derivative Meromorphic Functions Involving the Polylogarithm Function

Abstract

The aim of this research study is to establish a novel subclass of meromorphic functions in the mean of q-derivatives in combination with the well-known polylogarithm function. Two additional subfamilies for this class are also defined. Furthermore, the coefficient inequality and distortion bounds are highlighted. Finally, the convex families and related set structures are thoroughly investigated.

Keywords

• polylogarithm function (or de Jonquière’s function)
• meromorphic functions
• hadamard product
• <i>q</i>-derivatives
• convex families
• connected sets