The Sharp Bounds of the Third-Order Hankel Determinant for Certain Analytic Functions Associated with an Eight-Shaped Domain
Lei Shi, Meshal Shutaywi, Nasser Alreshidi, Muhammad Arif, Syed Muhammad Ghufran
Abstract
The main focus of this research is to solve certain coefficient-related problems for analytic functions that are subordinated to a unique trigonometric function. For the class Ssin*, with the quantity zf′(z)f(z) subordinated to 1+sinz, we obtain an estimate on the initial coefficient a4 and an upper bound of the third Hankel determinant. For functions in the class BTsin, with f′(z) lie in an eight-shaped domain in the right-half plane, we prove that its upper bound of third Hankel determinant is 116. All the results are proven to be sharp.
Topics & Concepts
MathematicsDomain (mathematical analysis)Trigonometric functionsUpper and lower boundsClass (philosophy)Mathematical analysisAnalytic functionHankel transformFocus (optics)Function (biology)Plane (geometry)TrigonometryComplex planeOrder (exchange)Pure mathematicsBessel functionGeometryPhysicsEvolutionary biologyFinanceArtificial intelligenceEconomicsBiologyOpticsComputer scienceAnalytic and geometric function theoryMathematical functions and polynomialsDifferential Equations and Boundary Problems