Convolution properties for a family of analytic functions involvingq-analogue of Ruscheweyh differential operator

Ahmad, Khurshid; Arif, Muhammad; Liu, Jin Lin

doi:10.3906/mat-1812-6

Cited by 14 publications

(11 citation statements)

References 19 publications

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“…Mohammad and Darus [14] conducted an elaborate study of this operator. We have also seen similar work by Mahmood and Sokół [15] and Ahmad et al [16]. 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.…”

Section: Introductionsupporting

confidence: 63%

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: Introductionsupporting

confidence: 63%

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

et al. 2019

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“…They made significant contributions which gradually enhanced the attractiveness of this research area for potential researchers. For more literature on quantum calculus, see [17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

et al. 2020

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The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q-differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters.

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“…is the set of Janowski starlike functions; see [5]. Some interesting problems such as convolution properties, coefficient inequalities, sufficient conditions, subordinates results and integral preserving were discussed recently in [6][7][8][9][10] for some of the generalized families associated with circular domains.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

Islam

Khan

Ahmad³

et al. 2020

Mathematics

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The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and sufficient condition, the growth and distortion bound, closure theorem, convolution results, radii of starlikeness, extreme point theorem and the problem with partial sums for this class.

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Convolution properties for a family of analytic functions involvingq-analogue of Ruscheweyh differential operator

Abstract: The main object of the present paper is to investigate convolution properties for a new subfamily of analytic functions that are defined by q-analogue of Ruscheweyh differential operator. Several consequences of the main results are also given.

Cited by 14 publications

References 19 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

Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

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