Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limaçon Domain-Reference-Cited by-同舟云学术

Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limaçon Domain

Published:2023-06-27 Issue:7 Volume:7 Page:506
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Shaba Timilehin Gideon¹^ORCID,Araci Serkan²^ORCID,Adebesin Babatunde Olufemi¹,Tchier Fairouz³^ORCID,Zainab Saira⁴^ORCID,Khan Bilal⁵^ORCID

Affiliation:

1. Department of Mathematics, Landmark University, Omu-Aran 251103, Nigeria

2. Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep 27010, Türkiye

3. Mathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia

4. School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan

5. School of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China

Abstract

In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of this newly defined operator and define a new class of analytic and bi-univalent functions associated with the q-derivative operator. Furthermore, we find the initial Taylor–Maclaurin coefficients for these newly defined function classes of analytic and bi-univalent functions. We also show that these bounds are sharp. The sharp second Hankel determinant is also given for this newly defined function class.

Funder

King Saud University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/7/506/pdf

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