1955
DOI: 10.7146/math.scand.a-10430
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The derivative of a Schlichtfunction

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1959
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Cited by 28 publications
(8 citation statements)
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“…In connection with Theorem 2, it is of interest to mention a result of Lohwater, Piranian and Rudin [4]. These authors shows that for any sufficiently rapidly increasing sequence of integers 1 = ni < n2 < n3 < .…”
mentioning
confidence: 96%
See 1 more Smart Citation
“…In connection with Theorem 2, it is of interest to mention a result of Lohwater, Piranian and Rudin [4]. These authors shows that for any sufficiently rapidly increasing sequence of integers 1 = ni < n2 < n3 < .…”
mentioning
confidence: 96%
“…Now If el" and el(,"+t) are two points on the unit circle with 0 < t < w, and X + lk-1/2 < r/2 then (4) | gN(ei(a+t)) -gN(eta) I > e-x{cos(X + lk-1/2) -A12k-1c2} | Pn-. Using the above we get, I z I > 1, I g'(z) I < A{l z 1/(l z -1)}-(p = X/log k), and this gives the second part of Lemma 1.…”
mentioning
confidence: 99%
“…The corresponding problem for the derivatives is still unsolved for the general class S. For p < i, the inequality M p (r,f) < M p (r, k') is false in general [6]. For close-toconvex functions, Clunie and Duren [3], [4] showed M l {r ) f')<.M i {r 3 k t y i and, employing extreme point theory, MacGregor [7] generalised this to all p ^ 1.…”
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confidence: 99%
“…An immediate consequence of the above is that if f(z) is in s/, then f'(z) is in HK for all A satisfying 0<A<^-. However, there exists a univalent function/(z) such that/'(z) is not in 77A for any A>0 [10], hence Sf is not a subclass of si.…”
mentioning
confidence: 99%