Moduli difference of inverse logarithmic coefficients of univalent functions

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_nw^n defined on some disk |w|≤ r_0(f). The inverse logarithmic coefficients Γ_n, n ∈ℕ, of f are defined by the equation log(F(w)/w)=2∑_n=1^∞Γ_nw^n, |w|<1/4. In this paper, we find the sharp upper and lower bounds for moduli difference of second and first inverse logarithmic coefficients, i.e., |Γ_2|-|Γ_1| for functions in class 𝒮 and for functions in some important subclasses of univalent functions.