On the Dziok–Srivastava operator under multivalent analytic functions

Piejko, Krzysztof; Sokół, Janusz

doi:10.1016/j.amc.2005.11.039

Cited by 18 publications

(4 citation statements)

References 6 publications

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“…Here, in this concluding section, we record several further applications of Theorems 1 to 4. By using Equation (15) Corollary 20 If f (z) ∈ A p satisfies Equation (16) and…”

Section: Remarkmentioning

confidence: 99%

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Subordinations for multivalent analytic functions associated with the Dziok–Srivastava operator

Srivástava

Du²,

2009

Integral Transforms and Special Functions

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Let A p (p ∈ N := {1, 2, 3, . . .}) be the class of functions f given bywhich are analytic in the open unit disk U. Making use of the method of differential subordinations, we obtain some sufficient conditions for f (z) ∈ A p involving the Dziok-Srivastava operator to satisfy certain subordination properties. The results presented here are shown not only to generalize the main results in several earlier investigations, but also to give rise to many other new results.

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“…Here, in this concluding section, we record several further applications of Theorems 1 to 4. By using Equation (15) Corollary 20 If f (z) ∈ A p satisfies Equation (16) and…”

Section: Remarkmentioning

confidence: 99%

“…In recent years, several authors obtained many interesting results involving the DziokSrivastava linear operator H l,m p (α 1 ) (see [1], [4] to [9], [11], [15], [16], [19], and [23] [2,3,14,17,20,21,24]. Here, and elsewhere in this investigation, we make the notation simple by writing…”

Section: Introduction Definitions and Preliminariesmentioning

confidence: 95%

Subordinations for multivalent analytic functions associated with the Dziok–Srivastava operator

Srivástava

Du²,

2009

Integral Transforms and Special Functions

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“…/ Theorem 14: Let ( ) then , ( )-( ), S.S. Miller, P.T. Mocanu [4,5]. The definitions given below are of the fractional calculus studied by , S. Ruscheweyh [4].…”

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confidence: 99%

Certain Family of Multivalent Functions Associated With Subordination

Mahmood¹,

Shihab²,

Jassim³

2020

IHJPAS

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“…Many interesting subclasses of analytic functions, associated with the Dziok-Srivastava operator, were studied recently by (for example) Srivastava et al [8], [9], [17], [20], (see also [3], [4], [18]). …”

Section: Introductionmentioning

confidence: 99%

Applications of convolution properties

Trojnar-Spelina

2013

Demonstratio Mathematica

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Abstract. K. I. Noor (2007 Appl. Math. Comput. 188, 814-823) has defined the classes Q k (a, b, λ, γ) and T k (a, b, λ, γ) of analytic functions by means of linear operator connected with incomplete beta function. In this paper, we have extended some of the results and have given other properties concerning these classes. IntroductionLet A denote the class of functions f analytic in the open unit disc U = {z : |z| < 1} and normalized by the conditions f (0) = f (0) − 1 = 0. Denote by S * (α), K(α)(0 ≤ α < 1) the subfamilies consisting of functions in A that are starlike of order α and convex of order α respectively. For 0 ≤ γ < 1 and k ≥ 2 let P k (γ) denote the class of functions p analytic in U satisfying the conditions p(0) = 1 andwhere z = re iθ . The class P k (γ) has been introduced by Padmanabhan and Parvatham (see [16]). For special choices of parameters, we obtain the known classes of functions. For example, for k = 2 we have the class P(γ) of functions with real part greater than γ and consequently, for k = 2 and γ = 0 we obtain the class of functions with positive real part. For γ = 0 we have the class P k defined by Pinchuk [19]. From (1), we conclude that p(z) = 1 2 2π 0 1 + (1 − 2γ)ze −it 1 − ze −it dµ(t)2010 Mathematics Subject Classification: 30C45.

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On the Dziok–Srivastava operator under multivalent analytic functions

Cited by 18 publications

References 6 publications

Subordinations for multivalent analytic functions associated with the Dziok–Srivastava operator

Subordinations for multivalent analytic functions associated with the Dziok–Srivastava operator

Certain Family of Multivalent Functions Associated With Subordination

Applications of convolution properties

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