Bi-Univalent Functions Defined on a Shell-Shaped Region.

Source abstract

In this article, we introduce a basic class of analytic functions linked with a Shell-Shaped Region using the principle of subordination and using q-calculus where q is in (0,1). Moreover, we apply the well known method of Ma and Minda to investigate a novel subclass of bi-univalent functions. Using a geometric approach, we prove that the class is nonempty. We then derive the best estimates for the Taylor-Maclaurin coefficients |\vartheta_{2}| and |\vartheta{3}|. Furthermore, we solve the Fekete-Szego functional. The study examines a shell-shaped image domains using the subordination principle under q-calculus, supported by illustrative geometric plots.