Some families of multivalent functions

Aouf, M. K.; Hossen, H. M.; Srivástava, H. M.

doi:10.1016/s0898-1221(00)00063-8

Cited by 23 publications

(11 citation statements)

References 4 publications

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“…We note that S * p (α) ⊆ S * p (0) ≡ S * p and K p (α) ⊆ K p (0) ≡ K p (0 α < p), where S * p and K p denote the subclasses of A p consisting of functions which are p-valently starlike in U and p-valently convex in U, respectively (see, for details, [5]; see also [20] and [1]). …”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On certain subclasses of multivalent functions associated with an extended fractional differintegral operator

Patel

Mishra

2007

Journal of Mathematical Analysis and Applications

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In the present paper an extended fractional differintegral operator Ω (λ,p) z (−∞ < λ < p + 1; p ∈ N), suitable for the study of multivalent functions is introduced. Various mapping properties and inclusion relationships between certain subclasses of multivalent functions are investigated by applying the techniques of differential subordination. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

On certain subclasses of multivalent functions associated with an extended fractional differintegral operator

Patel

Mishra

2007

Journal of Mathematical Analysis and Applications

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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%

“…Also, by T (p, k; η) (η ∈ R) we denote the class of functions f ∈ A (p, k) of the form (1) for which all of non-vanishing coefficients satisfy the condition (4) arg(a n ) = π + (p − n)η (n = k, k + 1, . .…”

Section: Introductionmentioning

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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“…The classes Sp(n, a) and Kp(n, a) were studied by Aouf et al [2] (see also [14]). In particular, the class Sp (l,a) = S*(a)(0 < a < p;p G N) was considered by Patil and Thakare [15].…”

Section: It Follows From (12) and (13) That F(z) E Kp(n A) And G S*(mentioning

confidence: 99%