Logarithmic Inverse Coefficients and Moduli Differences of Janowski Class

Abstract

In this paper, we study the sharp bounds of the first three logarithmic inverse coefficients for Janowski convex class $\mathcal{C}(A, B)$. We also derive sharp upper and lower bounds of $\bigl|\,γ_2 \,\bigr|-\bigl|\,γ_1\,\bigr|$ and $\bigl|\,Γ_2 \,\bigr|-\bigl|\,Γ_1\,\bigr|$ for functions in the class $\mathcal{C}(A, B)$. Furthermore, a sharp estimate for the second Hankel determinant associated with the logarithmic inverse coefficients for functions in $\mathcal{C}(A, B)$ is obtained.