SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS

2019/01/29 by NAK EUN CHO, Nak Eun Cho, BOGUMIŁA KOWALCZYK +3 · 5 citations
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Algebraic and Geometric Analysis

paper · doi:10.1017/s0004972718001429

Abstract

We apply the Schwarz lemma to find general formulas for the third coefficient of Carathéodory functions dependent on a parameter in the closed unit polydisk. Next we find sharp estimates of the Hankel determinant H_2,2 and Zalcman functional J_2,3 over the class CV of analytic functions f normalised such that Re\(1-z²)f^′ (z)\>0 for z∈ \mathbbD:=\z∈ ℂ:|z|<1\ , that is, the subclass of the class of functions convex in the direction of the imaginary axis.

Citations

• Early coefficients of the inverse of a regular convex function
• On the Theory of Univalent Functions

Cited by

• SECOND HANKEL DETERMINANT FOR LOGARITHMIC INVERSE COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS
• Coefficient Problems and Sharp Determinant Estimates for the Class S^*_q1
• On Coefficient problems for classes S_e^∗ and C_e
• Higher-Order Schippers-Schwarzian Derivatives for Non-Circular Starlike Functions
• Coefficient Problems for a Ma-Minda Convex Class Associated with the Normalized Arcsine Mapping

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• Coefficient Problems for a Ma-Minda Convex Class Associated with the Normalized Arcsine Mapping
• Some properties of the class U
• The sharp bound of the third order Hankel determinant for inverse of Ozaki close-to-convex functions
• THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS
• On a certain class of starlike functions