New distortion theorems for functions of positive real part and applications to the partial sums of univalent convex functions

Bernardi, S. D.

doi:10.1090/S0002-9939-1974-0357755-9

New distortion theorems for functions of positive real part and applications to the partial sums of univalent convex functions
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by S. D. Bernardi

Proc. Amer. Math. Soc. 45 (1974), 113-118

DOI: https://doi.org/10.1090/S0002-9939-1974-0357755-9

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Abstract:

New distortion theorems are obtained for the class of functions $p(z) = 1 + {c_n}{z^n} + \cdots (n \geq 1)$ which are analytic and $\text {Re} p(z) > \alpha (0 \leq \alpha < 1)$ in the unit disk $|z| < 1$. These are used to obtain new results regarding the partial sums of univalent convex functions.

References

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Univalent convex maps of the unit disk

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