Construction of new analytic function families via a novel q-differential perspective

The fundamental aim of this paper is to apply a novel q-differential operator in $$\mathbb {U}$$ and to make use of starlike functions to define a new subfamily of analytic functions in $$\mathbb {U}$$ . The goals of the study are to establish the characterization properties of this new class of bi-univalent functions, and to determine their covering, distortion, and growth characteristics. In addition, certain closure, inclusion, subordination characteristics, and radius problems are investigated for functions belonging to this new class of bi-univalent functions. The proposed class consists of analytic functions in $$\mathbb {U}$$ , and the extremal functions corresponding to this family are also obtained.