On Bounded Boundary and Bounded Radius Rotations

Noor, Khalida İnayat; Ul-Haq, Wasim; Arif, Muhammad; Mustafa, Saima

doi:10.1155/2009/813687

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Introduction3

Sarfraz Nawaz Malik Mohsan Raza Muhammad Arif and Saqib Hu1

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Cited by 24 publications

(12 citation statements)

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“…This class was introduced and studied in details by Moulis [1]. For l = 0, we obtain the class V k (σ ) of analytic functions with bounded boundary rotations of order s studied by Padmanabhan et al [2] and when s = 0 and l = 0, we get the class V k discussed by Paatero [3], see also [4][5][6][7][8]. Also it can easily be shown that…”

Section: Introductionmentioning

confidence: 78%

Hankel determinant problem of a subclass of analytic functions

2012

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Section: Introductionmentioning

confidence: 78%

Hankel determinant problem of a subclass of analytic functions

2012

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“…This result has been proved in [5]. (iii) For p = 1, it follows from Theorem 2.3 that f ∈ V k (α) is in R k (β 1 ), where β 1 is given by (2.7); see [8].…”

mentioning

confidence: 80%

On multivalent functions of bounded radius rotations

Noor

Al-Said

2011

Applied Mathematics Letters

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“…These classes were studied by Noor [10,11,15] in some details. Now we define the classes β −U T k (γ) and β −U T * k (γ) of analytic functions by using the concepts of bounded boundary rotations and bounded radius rotations as follows.…”

Section: Sarfraz Nawaz Malik Mohsan Raza Muhammad Arif and Saqib Humentioning

confidence: 99%

Coefficients estimates of some subclasses of analytic functions related with conic domain

Raza

Arif

Hussain

2013

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In this paper, the authors determine the coefficient bounds for functions in certain subclasses of analytic functions related with the conic regions, which are introduced by using the concept of bounded boundary and bounded radius rotations. The effect of certain integral operator on these classes has also been examined. Sarfraz Nawaz Malik, Mohsan Raza, Muhammad Arif and Saqib HussainLet A be the class of functions of the form 1) which are analytic in the unit disc E = {z : |z| < 1}. Also let K γ and C * γ denote the well-known classes of close-to-convex and quasi-convex functions of complex order γ (γ = 0) respectively, see for details [2,12]. Kanas and Wisniowska [5,6] studied the classes of β-uniformly convex functions denoted by β − U CV and the corresponding class of β-starlike functions β − ST related by the Alexandar type relation. Later Acu [1] considered the class of β-uniformly close-to-convex functions, denoted by β − U K and is defined as:

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On Bounded Boundary and Bounded Radius Rotations

Cited by 24 publications

References 5 publications

Hankel determinant problem of a subclass of analytic functions

Hankel determinant problem of a subclass of analytic functions

On multivalent functions of bounded radius rotations

Coefficients estimates of some subclasses of analytic functions related with conic domain

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