To obtain some estimates of the coefficients of regular and single-leaf functions in a circle, we use the Grunsky condition: for a single-leaf function in a circle that is regular in it, it is necessary and sufficient that the inequality be fulfilled...

Let S(k), k=1, 2, . . . . is the class of functions, regular and univalent in the disk |z| < 1. Sα(k) is a subclass of functions S(k). This class of functions is non-empty for any αk, 0 < αk ≤ 2/k. …