On Lemniscate of Bernoulli of q-Janowski type

Abstract

In this article, we introduce the q-analogue of functions characterized by the lemniscate of Bernoulli in the right-half plane and define the class $\mathbb{L}^{\ast}_{q}(A, B)$. Furthermore, we study the geometric properties of this class, which include coefficient inequalities, subordination factor sequence property, radii results and Fekete-Szeg$\ddot{\textup{o}}$ problems. Some deductions of our results show relevant connections between this present work and the existing ones in many literature. It is worthy of note that some of our results are sharp.

Keywords

• Univalent functions, Schwarz functions, Lemniscate of Bernoulli, Subordination, Janowski Functions