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.

Coefficient Inequalities of q-Bi-Univalent Mappings Associated with q-Hyperbolic Tangent Function

“…Remarkably, as q approaches 1, the D q reduces to the classical derivative. For more details and recent applications of the q-fractional derivative, we refer the readers to [15][16][17][18][19][20][21] and the references therein.…”