Analytic Functions Related to a Balloon-Shaped Domain
Adeel Ahmad, Jianhua Gong, Isra Al-Shbeil, Akhter Rasheed, Asad Ali, Saqib Hussain
Abstract
One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions X defined in the new domain, including the sharp estimates for the coefficients a2,a3, and a4, and for three second-order and third-order Hankel determinants, H2,1X,H2,2X, and H3,1X. The optimality of each obtained estimate is given as well.
Topics & Concepts
Analytic functionDomain (mathematical analysis)MathematicsQuotientComplex-valued functionClass (philosophy)Order (exchange)Analytic element methodFunction (biology)Mathematical analysisPure mathematicsNon-analytic smooth functionGlobal analytic functionApplied mathematicsComputer sciencePhysicsEvolutionary biologyArtificial intelligenceFinite element methodFinanceEconomicsThermodynamicsBiologyAnalytic and geometric function theoryMathematical functions and polynomialsHolomorphic and Operator Theory