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Mat. Zametki, 1970, Volume 7, Issue 5, Pages 581–592 (Mi mz9542)  

This article is cited in 4 scientific papers (total in 4 papers)

Radii of convexity and close-to-convexity of certain integral representations

F. G. Avkhadiev

V. I. Ul'yanov Lenin Kazan State University

Abstract: Strict upper bounds are determined for $|s(z)|$, $|\mathrm{Re} s(z)|$, and $|\mathrm{Im} s(z)|$ in the class of functions $s(z)=a_nz^n+a_{n+1}z^{n+1}+…$ ($n\geqslant1$) regular in $|z|<1$ and satisfying the condition
$$ |u(\theta_1)-u(\theta_2)|\leqslant K|\theta_1-\theta_2|, $$
where $u(\theta)=\mathrm{Re} s(e^{i\theta})$, $K>0$, and $\theta_1$ and $\theta_2$ are arbitrary real numbers. These bounds are used in the determination of radii of convexity and close-to-convexity of certain integral representations.

Full text: PDF file (1080 kB)

English version:
Mathematical Notes, 1970, 7:5, 350–357

Bibliographic databases:

UDC: 517.5
Received: 23.05.1969

Citation: F. G. Avkhadiev, “Radii of convexity and close-to-convexity of certain integral representations”, Mat. Zametki, 7:5 (1970), 581–592; Math. Notes, 7:5 (1970), 350–357

Citation in format AMSBIB
\Bibitem{Avk70}
\by F.~G.~Avkhadiev
\paper Radii of convexity and close-to-convexity of certain integral representations
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 5
\pages 581--592
\mathnet{http://mi.mathnet.ru/mz9542}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=286990}
\zmath{https://zbmath.org/?q=an:0204.39105|0198.42101}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 5
\pages 350--357
\crossref{https://doi.org/10.1007/BF01123846}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. F. G. Avkhadiev, L. A. Aksent'ev, “The main results on sufficient cjnditions for an analytic function to be schlicht”, Russian Math. Surveys, 30:4 (1975), 1–63  mathnet  crossref  mathscinet  zmath
    2. F. F. Maier, “Tochnye otsenki dlya regulyarnykh v kruge funktsii”, Konstr. teor. funkts. i funkts. anal., 4, Izd-vo Kazanskogo un-ta, Kazan, 1983, 33–41  mathnet  mathscinet  zmath
    3. F. F. Maier, “Podchinenie v nekotorykh klassakh analiticheskikh funktsii i odnolistnaya razreshimost obratnykh kraevykh zadach”, Konstr. teor. funkts. i funkts. anal., 5, Izd-vo Kazanskogo un-ta, Kazan, 1985, 61–72  mathnet  mathscinet  zmath
    4. I. R. Nezhmetdinov, “Tochnye otsenki garmonicheskikh funktsii i ikh proizvodnykh v kruge”, Konstr. teor. funkts. i funkts. anal., 5, Izd-vo Kazanskogo un-ta, Kazan, 1985, 72–80  mathnet  mathscinet  zmath
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