The value regions of initial coefficients in a certain class of meromorphic functions

Let $M_{k,\lambda}$ ($0\le\lambda\le1$, $k\ge2$) be the class of functions
$$ f(z)=1/z+a_0+a_1z+\dots, $$
that are regular and locally univalent for $0<|z|<1$ and satisfy the condition
$$ \lim_{r\to1-}\int_0^{2\pi}|\operatorname{Re}J+\lambda(re^{i\theta})|\,d\theta\le k\pi, $$
where
$$ J_\lambda(z)=\lambda(1+zf''(z)/f'(z))+(1-\lambda)zf'(z)/f(z). $$
In the class $M_{k,\lambda}$ we consider sorne coefficient problems and problems concerning distortion theorems. Bibliography: 6 titles.