Some applications of a q-analogue of the Ruscheweyh type operator for multivalent functions

Arif, Muhammad; Srivástava, H. M.; Umar, Sadaf

doi:10.1007/s13398-018-0539-3

Cited by 55 publications

(34 citation statements)

References 24 publications

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“…Recently, new thoughts by Maslina in [17] were used to create a novel differential operator called generalized q-differential operator with the help of q-hypergeometric functions where the authors conducted an in-depth study of applications of this operator. For further information on the extensions of different operators in q-analog, we direct the readers to [18][19][20][21][22]. The aim of the present article is to introduce a new integral operator in q-analog for multivalent functions using Hadamard product and then study some of its useful applications.…”

Section: Introductionmentioning

confidence: 99%

Some Applications of a New Integral Operator in q-Analog for Multivalent Functions

et al. 2019

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This paper introduces a new integral operator in q-analog for multivalent functions. Using as an application of this operator, we study a novel class of multivalent functions and define them. Furthermore, we present many new properties of these functions. These include distortion bounds, sufficiency criteria, extreme points, radius of both starlikness and convexity, weighted mean and partial sum for this newly defined subclass of multivalent functions are discussed. Various integral operators are obtained by putting particular values to the parameters used in the newly defined operator.

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Section: Introductionmentioning

confidence: 99%

Some Applications of a New Integral Operator in q-Analog for Multivalent Functions

et al. 2019

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“…Many researchers contributed in the development of the theory by introducing certain classes with the help of q-calculus. For some details about these contributions, see [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

q-Analogue of Differential Subordinations

Ul-Haq¹,

Raza²,

Arif³

et al. 2019

Mathematics

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In this article, we study differential subordnations in q-analogue. Some properties of analytic functions in q-analogue associated with cardioid domain and limacon domain are considered. In particular, we determine conditions on α such that 1 + α z ∂ q h z h z n ( n = 0 , 1 , 2 , 3 ) are subordinated by Janowski functions and h z ≺ 1 + 4 3 z + 2 3 z 2 . We also consider the same implications such that h z ≺ 1 + 2 z + 1 2 z 2 . We apply these results on analytic functions to find sufficient conditions for q-starlikeness related with cardioid and limacon.

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“…Many researchers contributed to the development of the theory by introducing certain classes with the help of q-calculus. For some details about these contributions, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. We contribute to the subject by studying the q-integral operator in the conic region.…”

Section: Introductionmentioning

confidence: 99%

“…A m z m be the extremal function in class K − U ST µ q (γ) and h k,γ be of the form (12). Then, these functions can be related by the relation:…”

Section: Introductionmentioning

confidence: 99%

Class of Analytic Functions Defined by q-Integral Operator in a Symmetric Region

et al. 2019

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The aim of the present paper is to introduce a new class of analytic functions by using a q-integral operator in the conic region. It is worth mentioning that these regions are symmetric along the real axis. We find the coefficient estimates, the Fekete-Szegö inequality, the sufficiency criteria, the distortion result, and the Hankel determinant problem for functions in this class. Furthermore, we study the inverse coefficient estimates for functions in this class.Let f and g be analytic functions in D. Then, f is said to be subordinate to g, written as f (z) ≺ g(z), if there exists a function w analytic in D with w(0) = 0 and |w (z) | < 1 such that f (z) = g(w(z)). Moreover, if g is univalent in D, then the following equivalent relation holds:The classes of k-uniformly starlike and k-uniformly convex functions were introduced by Kanas and Wiśniowska [1,2]. A function f ∈ S is in k − ST , if and only if:

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Some applications of a q-analogue of the Ruscheweyh type operator for multivalent functions

Cited by 55 publications

References 24 publications

Some Applications of a New Integral Operator in q-Analog for Multivalent Functions

Some Applications of a New Integral Operator in q-Analog for Multivalent Functions

q-Analogue of Differential Subordinations

Class of Analytic Functions Defined by q-Integral Operator in a Symmetric Region

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