A class of distortion theorems involving certain operators of fractional calculus

Srivástava, H. M.; Saigo, Megumi; Owa, Shigeyoshi

doi:10.1016/0022-247x(88)90215-6

Cited by 85 publications

(43 citation statements)

References 3 publications

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“…the generalized fractional calculus operators and are defined below (cf., e.g., [9] and [16]). where / is an analtyic function in a simply -connected region of the zplane containing the origin, and the multiplicity of (ζ -ζ) μ~1 is removed by requiring log(z -ζ) to be real when (z -ζ) > 0 , provided further that ^J q ™ /(2) (η<μ<η+1;η£ Ν) (G> max{0,7 -η} -1), where / is constrained, and the multiplicity of (zis removed, as in Definition 1, and G is given by the order estimate (8.3).…”

Section: Properties Associated With Generalized Fractional Calculus Omentioning

confidence: 99%

Some Properties of a Subclass of Uniformly Convex Functions With Negative Coefficients

Aouf¹,

Mostafa²

2008

Demonstratio Mathematica

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Abstract. The aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close -to -convexity, starlikeness and convexity for functions belonging to the subclass TS\ (n,a,β) of uniformly convex functions with negative coefficients. We also derive many results for the modified Hadamard products of functions belonging to the class TS\ (n,a, β), and obtain several interesting distortion theorems for certain fractional operators of functions in this class. Finally, we consider integral operators associated with functions in this class.

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Section: Properties Associated With Generalized Fractional Calculus Omentioning

confidence: 99%

Some Properties of a Subclass of Uniformly Convex Functions With Negative Coefficients

Aouf¹,

Mostafa²

2008

Demonstratio Mathematica

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“…For real numbers α > 0, β and γ, the generalized fractional integral associated with Gauss hypergeometric function is defined by (see Saigo (1978) and Srivastava et al (1988)):…”

Section: A Generalization Of the Stfppmentioning

confidence: 99%

Saigo space–time fractional Poisson process via Adomian decomposition method

Kataria

Vellaisamy

2017

Statistics & Probability Letters

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Abstract. We obtain the state probabilities of various fractional versions of the classical homogeneous Poisson process using an alternate and simpler method known as the Adomian decomposition method (ADM). Generally these state probabilities are obtained by evaluating probability generating function using Laplace transform. A generalization of the space and time fractional Poisson process involving the Caputo type Saigo differential operator is introduced and its state probabilities are obtained using ADM.

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“…Saigo's fractional calculus operator I α,β,η 0,z f (z) of f (z) ∈ A is defined by Srivastava et al [19] (see also, Saigo [14]) as follows:…”

Section: Distortion Theoremmentioning

confidence: 99%

“…In order to derive the inequalities involving Saigo's fractional operators, we need the following lemma due to Srivastava, Saigo and Owa [19].…”

Section: Distortion Theoremmentioning

confidence: 99%

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Geometric properties and neighborhood results for a subclass of analytic functions involving Komatu integral

Agarwal¹,

Paliwal²,

Parihar

2017

Stud. Univ. Babes-Bolyai Math.

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Abstract. In this paper, a subclass of analytic function is defined using Komatu integral. Coefficient inequalities, Fekete-Szegö inequality, extreme points, radii of starlikeness and convexity and integral means inequality for this class are obtained. Distortion theorem for the generalized fractional integration introduced by Saigo are also obtained. The inclusion relations associated with the (n,µ)-neighborhood also have been found for this class.Mathematics Subject Classification (2010): 47A15, 46A32, 47D20.

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A class of distortion theorems involving certain operators of fractional calculus

Cited by 85 publications

References 3 publications

Some Properties of a Subclass of Uniformly Convex Functions With Negative Coefficients

Some Properties of a Subclass of Uniformly Convex Functions With Negative Coefficients

Saigo space–time fractional Poisson process via Adomian decomposition method

Geometric properties and neighborhood results for a subclass of analytic functions involving Komatu integral

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