A radius of convexity problem
1983 ◽
Vol 28
(3)
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pp. 433-439
Keyword(s):
The authors determine the sharp radius of convexity for functions analytic in the unit disc having power series representation of the form f(z) = z + an+1zn+1 + an+2zn+2 + … where an+1 is fixed and such that zf′(z)/f(x) = (1 + Aw(z))/(1 + Bw(z)), −1 ≤ B < 0 < A ≤ 1 where w(z) is an analytic function satisfying the conditions of Schwarz's lemma, in the case A + B ≥ 0. The estimate obtained is an improvement over the corresponding result obtained by Mogra and Juneja for functions analytic and starlike in the unit disc, with missing coefficients where the initial non-vanishing coefficient is fixed.
1981 ◽
Vol 24
(3)
◽
pp. 381-388
◽
Keyword(s):
2002 ◽
Vol 32
(1)
◽
pp. 29-40
Keyword(s):
1984 ◽
Vol 7
(3)
◽
pp. 443-454
2020 ◽
Vol 370
◽
pp. 124911
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1974 ◽
Vol 45
(1)
◽
pp. 136-141
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Keyword(s):
Keyword(s):
2020 ◽
Vol 68
(7)
◽
pp. 5696-5701
Keyword(s):