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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On certain extremal problems for functions with positive real part
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by Stephan Ruscheweyh and Vikramaditya Singh PDF
Proc. Amer. Math. Soc. 61 (1976), 329-334 Request permission

Abstract:

For the class $P$ of analytic functions $p(z),p(0) = 1$, with positive real part in $|z| < 1$, a type of extremal problems is determined which can be solved already within the set $p(z) = (1 + \varepsilon z)/(1 - \varepsilon z),\;|\varepsilon | = 1$. One problem of this kind is to find the largest number $\rho (s,\;\mu )$ such that \[ \operatorname {Re} \{ p(z) + szp’(z)/(p(z) + \mu )\} > 0,\] $|z| \leqslant \rho (s,\;\mu )$, for all $p \in P,\; - 1 \ne \mu \in {\mathbf {C}},\;s > 0$. Sharp upper bounds for two other functionals over $P$ are also given.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 61 (1976), 329-334
  • MSC: Primary 30A32
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0425102-1
  • MathSciNet review: 0425102