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Zbl 0835.30006
Dixit, K.K.; Pal, S.K.
On a class of univalent functions related to complex order. (English)
[J] Indian J. Pure Appl. Math. 26, No.9, 889-896 (1995). ISSN 0019-5588; ISSN 0975-7465/e

Authors' summary: In this paper the class $R^\ell (A,B)$ ($\ell\ne 0$ complex), of functions of the form $f(z)= z+ \sum_{n=2}^\infty a_n z^n$ regular in the open unit disk $D$ such that $$1+ {1\over b} (f' (z)- 1)\ \prec\ {{1+ Az} \over {1+ Bz}},$$ where $-1\leq B< A\leq 1$ is introduced. Sharp coefficient estimates, sufficient conditions in terms of coefficients, distortion theorem, maximization theorem for the class $R^\ell (A, B)$ are proved.
[R.Parvatham (Madras)]

MSC 2000:: *30C45 Special classes of univalent and multivalent functions

Keywords: complex order

Cited in: Zbl 1014.30012

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