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 $\left|{\hat{I}}_2^3\right|-\left|{\hat{I}}_1^3\right|$ and $\left|\hat{I}{“}_2\right|-\left|\hat{I}{“}_1\right|$ 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.

Preliminary version