On certain subclasses of analytic functions associated with hypergeometric functions (original) (raw)
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International Journal of Mathematics and Mathematical Sciences, 2010
Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the class TS l m α, β, γ . In particular, we obtain integral means inequalities for the function f that belongs to the class TS l m α, β, γ in the unit disc.
Generalized hypergeometric functions associated with k-uniformly convex functions
Computers & Mathematics with Applications, 2002
For a certain linear operator which is defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function, the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as (for example) /c-uniformly convex functions and /c-starlike functions. Relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out.
Subclasses of analytic functions associated with the generalized hypergeometric function
Computers & Mathematics with Applications, 2009
Using the generalized hypergeometric function, we study a class Φ p k (q, s; A, B, λ) 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 Φ p k (q, s; A, B, λ).
Classes of analytic functions associated with the generalized hypergeometric function
Applied Mathematics and Computation, 1999
Using the generalized hypergeometric function, we introduce and study a class of analytic functions with negative coecients. Coecients 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. Ó . 0096-3003/99/$ ± see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 0 9 6 -3 0 0 3 ( 9 8 ) 1 0 0 4 2 -5
Certain New Subclasses of Analytic Functions Involving Generalized Hypergeometric Function
Journal of the Nigerian Mathematical Society, 2019
In this work the author considered new subclasses of analytic univalent functions using certain linear operator. With the operator, the author was able to study several new and existing subclasses of analytic univalent functions in the unit disk. The results presented in this paper include, coefficient estimates (which were later used to investigate certain subclasses of analytic functions with fixed finitely many coefficients) and distortion theorems for functions belonging to these subclasses. Furthermore, some relationships between these subclasses were also discussed.