Higher-Order Schippers-Schwarzian Derivatives for Non-Circular Starlike Functions

2026/07/28 by Pradip Das, Paweł Zaprawa, Nabadwip Sarkar
Mathematics · #math.CV

paper · pdf

arxiv created 2026/07/28 · arxiv updated 2026/07/30

Abstract

We find sharp upper bounds for the initial higher-order Schippers-Schwarzian derivatives σ₃(f)(0) and σ₄(f)(0) for several subclasses of univalent and starlike functions in the unit disk. The functions in these classes are defined by subordination to domains bounded by an exponential-sine curve, a cardioid, or a petal-shaped curve. We determine the sharp bounds and find the corresponding extremal functions for each invariant in these subclasses. As an application, we also obtain sharp bounds for the initial Grunsky coefficients ω_1,1 and ω_1,2.

Citations

• On estimation of Hankel determinants for certain class of starlike functions
• SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS
• Starlike functions associated with a cardioid
• Sharp norm estimate of Schwarzian derivative for a class of convex functions
• Distortion theorems for higher order Schwarzian derivatives of univalent functions
• Higher Schwarzian operators and combinatorics of the Schwarzian derivative
• Aharonov invariants and univalent functions
• Early coefficients of the inverse of a regular convex function
• On Some Classes of Bounded Univalent Functions

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