On the first coefficient regions of bounded univalent functions

On determining the points of the second coefficient body $(a_4,a_3,a_2)$ for bounded real univalent functions

“…The upper boundary arcs of 1:2-regions are continuations of the curve defined in (9). These are related with the formulae (20) and (21), p. 234 of [7] and with those on p. 10 of [4]. The coordinates involved appear to be the following:…”

“…The turning point in obtaining explicit results for bodies is the work done together with Kortram by using Grunsky type inequalities. The idea of this was first applied for (a s , 0 2 ) in S(b) [4] and was tested successfully for the second coefficient body in S R (b) yielding first algebraic parts of it [5]. However, in both cases the results remained partial and their completion needed much additional work and above all improving the inequalities available.…”

On the coefficient bodies of meromorphic univalent functions omitting a disc

“…In [3] the missing quantitative information is found by using Grunskytype inequalities in the most economic way, i.e. in so-called optimized form.…”

“…In [3] and [8] preliminary observations concerning the S(b)-body (a 3 , a 2 ) can be found. These are completed in [9] by using certain parameters obtained from the slitstructure of the extremal image domain f (U ).…”