Moduli difference of inverse logarithmic coefficients of univalent functions

2024/03/15 by Vasudevarao Allu, Amal Shaji, Allu, Vasudevarao +1
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2403.10031

openalex publication_date 2024/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be analytic in the unit disk and S be the subclass of normalized univalent functions with f(0) = 0, and f'(0) = 1. Let F be the inverse function of f, given by F(w)=w+∑_n=2^∞A_nwⁿ defined on some disk |w|≤ r₀(f). The inverse logarithmic coefficients Γ_n, n ∈ ℕ, of f are defined by the equation log(F(w)/w)=2∑_n=1^∞Γ_nwⁿ, |w|<1/4. In this paper, we find the sharp upper and lower bounds for moduli difference of second and first inverse logarithmic coefficients, \em i.e., |Γ₂|-|Γ₁| for functions in class S and for functions in some important subclasses of univalent functions.

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