Structural formulas and value regions of functionals in certain classes of regular functions

We study the structural properties of the class $M_{k,\lambda,b}$ ($k\ge2$, $0\le\lambda\le1$, $b\in\mathbb C\setminus\{0\}$) of functions $f(z)=z+\dots$ which are regular in $|z|<1$ and satisfy the conditions $f(z)f'(z)z^{-1}\ne0$ and $\lim_{r\to1-0}\int_0^{2\pi}|\operatorname{Re}J(z)|\,d\theta\le k\pi$ ($z=re^{i\theta}$), where
$$ J(z)=\lambda(1+b^{-1}zf''(z)/f'(z))+(1-\lambda)(b^{-1}zf'(z)/f(z)+1+b^{-1}). $$
The value regions of some functionals on this class are found. The case $\lambda=1$ was considered in our previous paper. Bibliography: 4 titles.