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The Third Hankel Determinant for Inverse Coefficients of Convex Functions | Synapse

April 23, 2026Bulletin of the Australian Mathematical Society0 citationsOpen Access

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The Third Hankel Determinant for Inverse Coefficients of Convex Functions

VAVASUDEVARAO ALLU SKShobhit KumarIndian Institute of Technology Bhubaneswar

Key Points

To determine the sharp upper bound for the third Hankel determinant related to inverse coefficients of convex univalent functions.
Analyzed the class of normalized analytic functions in the open unit disk.
Established conditions for convexity and univalence in the context of Hankel determinants.
Identified a precise upper bound for the third Hankel determinant of inverse coefficients.
Confirmed the relationship between convexity and the behavior of these determinants.

Abstract

Abstract Let A denote the class of normalised analytic functions f in the open unit disk D: =\z {C: |z|<1\} with f (0) =0 and f' (0) =1. A function f A is said to be convex if f (D) is convex. We establish a sharp upper bound for the third Hankel determinant corresponding to the inverse coefficients of convex univalent (that is, one-to-one) functions in the unit disk D.

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Cite This Study

ALLU et al. (Tue,) studied this question.

synapsesocial.com/papers/69e9b91385696592c86ebeff https://doi.org/https://doi.org/10.1017/s0004972726101130