The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator

Abstract

In this paper, we introduce and study a new subclass of normalized functions that are analytic and univalent in the open unit disk $ \mathbb{U} = \{z:z\in \mathcal{C}\; \; \text{and}\; \; |z| < 1\}, $ which satisfies the following geometric criterion: $ \begin{equation*} \Re\left(\frac{\mathcal{L}_{u, v}^{w}f(z)}{z}(1-e^{-2i\phi}\mu^2z^2)e^{i\phi}\right)>0, \end{equation*} $ where $ z\in \mathbb{U} $, $ 0\leqq \mu\leqq 1 $ and $ \phi\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $, and which is associated with the Hohlov operator $ \mathcal{L}_{u, v}^{w} $. For functions in this class, the coefficient bounds, as well as upper estimates for the Fekete-Szegö functional and the Hankel determinant, are investigated.

Keywords

• analytic functions
• univalent functions
• coefficient bounds
• fekete-szegöfunctional
• hohlov operator
• dziok-srivastava operator
• srivastava-wright operator
• fekete-szegöinequality
• hankel determinant
• basic q-calculus
• (p，q)-variation