Work

Third Hankel determinant for a subclass of bi-univalent functions related to balloon-shaped domain

Year: 2025

Type: article

Abstract: In this paper, we consider a subclass of bi-univalent functions, denoted by $ \mathbb{CS}_{\beth}^{\ast}(\gamma) $, which is defined via a balloon-shaped domain associated with the function $ \frac{2\sqrt{1+\varsigma}} {1+e^{-\varsigma}} $. We prove that this class is non-empty using illustrative mappings. We investigate upper bounds for the second- and third-order Hankel determinants, focusing on the functional $ H_{3}(1) $. In addition, we estimate the Taylor coefficients up to order $ l = 5 $, which are essential in obtaining bounds for the determinants. The balloon shape introduces new analytic features that enrich the behavior of the functions in this class. Several examples and special cases are offered to illustrate the flexibility of the outcomes.

Source: AIMS Mathematics

DOI: 10.3934/math.20251127

Authors: Mohammad El-Ityan, Tariq Al-Hawary, Basem Aref Frasin, Ibtisam Aldawish

Institutions: Al-Balqa Applied University, Al al-Bayt University, Imam Mohammad ibn Saud Islamic University

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

OpenAlex ID: W4415944146