Some thoughts on the theory of univalent functions

Abstract

The paper contains two different topics. The first topic deals with the coefficient problem. It is shown that for a certain type of rational functions (depending on a parameter q) the validity of Robertson's inequalities for n less than or equal to fq − 1 is sufficient to conclude Bieberbach/de Branges' inequalities for all n. In the second topic is studied the “stability of niceness” of Robertson's functional for n = 4.

AMS No.:

• Coefficients
• Robertson'
• functional
• “meeness”
• 30C50
• 30C55

^*E-mail: haakonwa#matstat.unit.no

^*E-mail: haakonwa#matstat.unit.no

Notes

^*E-mail: haakonwa#matstat.unit.no