## Classes of analytic functions associated with the generalized hypergeometric function,.(English)Zbl 0937.30010

Using the generalized hypergeometric function, the authors introduce and study a class of analytic functions with negative coefficients. Coefficients estimates, distortion theorems, extreme points, and the radii of convexity and starlikeness for this class are given. Relevant connections of these results with those in several earlier investigations are indicated.

### MSC:

 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 26A33 Fractional derivatives and integrals 33C20 Generalized hypergeometric series, $${}_pF_q$$
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### References:

 [2] Carlson, B. C.; Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15, 737-745 (1984) · Zbl 0567.30009 [3] Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math Soc., 49, 109-115 (1975) · Zbl 0303.30006 [4] Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135, 429-446 (1969) · Zbl 0172.09703 [5] Libera, R. J., Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16, 755-758 (1965) · Zbl 0158.07702 [6] Livingston, A. E., On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc., 17, 352-357 (1966) · Zbl 0158.07701 [7] Owa, S., On the distortion theorems. I, Kyungpook Math. J., 18, 53-59 (1978) · Zbl 0401.30009 [9] Srivastava, H. M.; Owa, S., Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions, Nagoya Math. J., 106, 1-28 (1987) · Zbl 0607.30014 [12] Dziok, J., Classes of analytic functions involving some integral operator, Folia Sci. Univ. Tech. Resoviensis, 20, 21-39 (1995) · Zbl 1076.30509 [13] Kim, Y. C.; Srivastava, H. M., Fractional integral and other linear operators associated with the Gaussian hypergeometric function, Complex Variables Theory Appl., 34, 293-312 (1997) · Zbl 0951.30010 [14] Srivastava, H. M.; Owa, S., A new class of analytic functions with negative coefficients, Comment. Math. Univ. St. Paul., 35, 175-188 (1986) · Zbl 0588.30012
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