A proof of Hall's conjecture on starlike mappings

Balasubramanian, R. ; Karunakaran, V. ; Ponnusamy, S. (1993) A proof of Hall's conjecture on starlike mappings Journal of the London Mathematical Society, s2-48 (2). pp. 278-288. ISSN 0024-6107.

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Official URL: http://jlms.oxfordjournals.org/content/s2-48/2/278...

Related URL: http://dx.doi.org/10.1112/jlms/s2-48.2.278

Abstract

In this paper we show that |ƒ(re|-1ƒr01(ue)|du≤ r-1arcsinr,0 < r<1 where f lies in the class of starlike functions of order ½, that is, which are regular and univalent for |z| < 1 and such that Re zf1(z)/f(z)>½ for |z<1|

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