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

Hari Mohan Srivastava; Timilehin Gideon Shaba; Gangadharan Murugusundaramoorthy; Abbas Kareem Wanas; Georgia Irina Oros; Hari Mohan Srivastava; Timilehin Gideon Shaba; Gangadharan Murugusundaramoorthy; Abbas Kareem Wanas; Georgia Irina Oros

doi:10.3934/math.2023016

AIMS Mathematics

2023, Volume 8, Issue 1: 340-360. doi: 10.3934/math.2023016

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Research article

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

1.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
3.
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
4.
Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy
5.
Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Kwara State, Nigeria
6.
Department of Mathematics, VIT University, Vellore 632014, Tamil Nadu, India
7.
Department of Mathematics, University of Al-Qadisiyah, Al Diwaniyah, Al-Qadisiyah, Iraq
8.
Department of Mathematics and Computer Science, University of Oradea, R-410087 Oradea, Romania

Received: 07 August 2022 Revised: 08 September 2022 Accepted: 20 September 2022 Published: 29 September 2022
MSC : Primary 30C45; Secondary 30C55, 33C05

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.
- 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
Citation: Hari Mohan Srivastava, Timilehin Gideon Shaba, Gangadharan Murugusundaramoorthy, Abbas Kareem Wanas, Georgia Irina Oros. The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator[J]. AIMS Mathematics, 2023, 8(1): 340-360. doi: 10.3934/math.2023016

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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.

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