Abbildungseigenschaften der arithmetischen Mittel der geometrischen Reihe

Applications of a lemma of Fejér to typically-real functions

“…which E. Egerväry [6] has shown to be Univalent and convex for 121 < 1, we obtain immediately a new proof of the following theorem of L. Fejer [5].…”

On Cesàro means, Kaplan classes and a conjecture of S.P. Robinson

“…It is known [3], that C (3) n (z) is convex univalent in D, for n ∈ N. Hence z(C (3) n+1 (z)) is a starlike univalent polynomial in D and cannot have zeros in D \ {0} (Koebe's one-quarter-theorem). Theorems 2 and 3 have now been established.…”

“…This is equivalent to −(n + 2) 3 U n+1 (y) + 2n(n + 1)(n + 2)U n (y) − n 3 U n−1 (y) −14n 2 − 28n − 16, with y = cos ϕ. Here U n stands for the Chebyshev polynomial of the second kind and degree n. Using the relation U n+1 (y) = 2 yU n (y) − U n−1 (y) we find the equivalent form U n (y) 2n(n + 1)(n + 2) − 2 y(n + 2) 3 + U n−1 (y) (n + 2) 3 …”

“…Note that Theorem 4 does not imply the linear accessibility of C (3) n (z, f ) for f ∈ L, in fact not even its univalence.…”