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Zbl 0611.33007
Owa, Shigeyoshi; Srivastava, H.M.
Univalent and starlike generalized hypergeometric functions. (English)
[J] Can. J. Math. 39, No.5, 1057-1077 (1987). ISSN 0008-414X; ISSN 1496-4279/e

Recently, {\it B. C. Carlson} and {\it D. B. Shaffer} [SIAM J. Math. Anal. 15, 737-745 (1984; Zbl 0567.30009)] introduced a linear operator and showed how this operator can be applied to the study of certain interesting classes of starlike, convex, and prestarlike hypergeometric functions. The object of the present paper is to prove some basic results involving univalent generalized hypergeometric functions, starlike generalized hypergeometric functions of order $\alpha$, and convex generalized hypergeometric functions of order $\alpha$. Moreover, a certain linear operator involving fractional calculus is introduced, and several general characterization theorems are given in terms of fractional calculus of functions belonging to some of the aforementioned classes of analytic functions.

MSC 2000:: *33C05 Classical hypergeometric functions
30C45 Special classes of univalent and multivalent functions
26A33 Fractional derivatives and integrals (real functions)

Keywords: starlike generalized hypergeometric functions of order $\alpha $; convex generalized hypergeometric functions of order $\alpha $

Citations: Zbl 0567.30009

Cited in: Zbl pre06121661 Zbl pre06083346 Zbl 1200.30014 Zbl 1132.30321 Zbl 1193.30027 Zbl 0897.30003 Zbl 0904.30006

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