Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function

Dziok, Jacek; Srivástava, H. M.

doi:10.1080/10652460304543

Cited by 218 publications

(106 citation statements)

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“…where f p+1,η (z) is defined by (7). see for example [1]- [5], [7] and [13]. Most of these classes were defined by using linear operators and special functions.…”

Section: Integral Means Inequalitiesmentioning

confidence: 99%

A new class of multivalent analytic functions defined by the Hadamard product

Dziok

2011

Demonstratio Mathematica

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Abstract. The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for classes of functions with two fixed points. Some remarks depicting consequences of the main results are also mentioned. IntroductionLet A denote the class of functions which are analytic in U = U(1), where U(r) = {z ∈ C: |z| < r}.and let A (p, k) (p, k ∈ N = {1, 2, 3...} , p < k) denote the class of functions f ∈ A of the formOne can obtain interesting results by applying normalization of the formwhere ρ is a fixed point of the unit disk U. In particular, for p = 1 we obtain Montel's normalization (cf.[8]). We see that for ρ = 0 the normalization (3) is the classical normalization.1991 Mathematics Subject Classification: 30C45.

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“…where f p+1,η (z) is defined by (7). see for example [1]- [5], [7] and [13]. Most of these classes were defined by using linear operators and special functions.…”

Section: Integral Means Inequalitiesmentioning

confidence: 99%

A new class of multivalent analytic functions defined by the Hadamard product

Dziok

2011

Demonstratio Mathematica

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“…is given by by Dziok-Srivastava [7]. Apart from deriving a set of coefficient bounds for each of these function classes, we establish several inclusion relationships involving the (n, δ )− negihborhoods of analytic functions with negative coefficients belonging to these subclasses.…”

mentioning

confidence: 99%

On certain classes of analytic functions of complex order defined by Dziok-Srivastava operator

Murugusundaramoorthy¹,

Rosy²,

Sivasubramanian³

2007

Journal of Mathematical Inequalities

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Abstract. Making use of the generalized hypergeometric functions, we introduced certain new subclasses of analytic functions defined by Dziok-Srivastava operator in the unit disc. The main object of the present paper is to investigate the various properties and characteristics of analytic functions belonging to the subclasses S n (l, m, λ , b, γ ) satisfying the inequalityis Dziok-Srivastava operator. Also let R n (l, m, λ , b, γ ) be an another subclass satisfying the inequalityis given by by Dziok-Srivastava [7]. Apart from deriving a set of coefficient bounds for each of these function classes, we establish several inclusion relationships involving the (n, δ )− negihborhoods of analytic functions with negative coefficients belonging to these subclasses. (2000): 30C45. Mathematics subject classification

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“…where [5]), includes (as its special cases) various other linear operators introduced and studied by Carlson and Shaffer [3], Ruscheweyh [10] and OwaSrivastava [9]. Motivated by earlier works of Aouf et al, [1] and Dziok and Raina [6] we define the following new subclass of T involving hypergeometric functions.…”

Section: Introductionmentioning

confidence: 99%

“…The notation l F m is quite useful for representing many well-known functions such as the exponential, the Binomial, the Bessel, the Laguerre polynomial (for example see [5] …”

Section: Introductionmentioning

confidence: 99%