A proof of Campbell's subordination conjecture

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A proof of Campbell’s subordination conjecture

In the early 70’s, D.M. Campbell published three papers on majorizationsubordination results for locally univalent functions. In particular, he showed that if F is linearly invariant of order α and if f is subordinate to F on {z : |z| < 1}, then f ′ is majorized by F ′ on {z : |z| < m(α)} where m(α) = α+ 1− √ α2 + 2α, provided α ≥ 1.65. He conjectured, in fact, that this result also held for 1....

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ژورنال

عنوان ژورنال: Complex Variables and Elliptic Equations

سال: 2009

ISSN: 1747-6933,1747-6941

DOI: 10.1080/17476930802669686