Resumen de On a conjecture for trigonometric sums and starlike functions

Stamatis Koumandos, Stephan Ruscheweyh

• We pose and discuss the following conjecture: let , and for ?(0,1] let µ*(?) be the unique solution µ(0,1] of Then for 0<µµ*(?) and we have . We prove this for , and in a somewhat weaker form, for . Far reaching extensions of our conjectures and results to starlike functions of order 1-µ/2 are also discussed. Our work is closely related to recent investigations concerning the understanding and generalization of the celebrated Vietoris' inequalities.