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∞Aₙwⁿ defined on some disk |w|≤ r₀(f). The inverse logarithmic coefficients Γₙ, n ∈ N, of f are defined by the equation log(F(w)/w)=2∑ₙ₌₁∞Γₙwⁿ,\,|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.,} |Γ₂|-|Γ₁| for functions in class S and for functions in some important subclasses of univalent functions.