In this paper, we find the necessary and sufficient conditions for functions zF (a, b; c; z) in the generalized class of Ξ² uniformly starlike and Ξ² uniformly convex functions of order Ξ± and also consequences of the results are pointed out.
Subclasses of analytic functions associated with the generalized hypergeometric function
β Scribed by M.K. Aouf; H.E. Darwish
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 591 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0898-1221
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β¦ Synopsis
Using the generalized hypergeometric function, we study a class Ξ¦ p k (q, s; A, B, Ξ») of analytic functions with negative coefficients. Coefficient estimates, distortion theorem, extreme points and the radii of close-to-convexity and convexity for this class are given. We also derive many results for the modified Hadamard product of functions belonging to the class Ξ¦ p k (q, s; A, B, Ξ»).
π SIMILAR VOLUMES
We deal with a class of integral transformations whose kernels contain the Clausenian hypergeometric function 3 F 2 (a 1 ; a 2 ; a 3 ; b 1 ; b 2 ; z). These transforms are deΓΏned in terms of integrals with respect to their parameters. It involves as particular cases the familiar Olevskii and general
Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), involving the generalized hypergeometric function, we introduce two novel subclasses β¦ p,q,s (Ξ± 1 ; A, B, Ξ») and β¦ + p,q,s (Ξ± 1 ; A, B, Ξ») of meromorphically multivalent functions of order Ξ» (0