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Volume 7
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Article

A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator

by
Muhammad Naeem
1,
Saqib Hussain
2,*,
Tahir Mahmood
1,
Shahid Khan
3 and
Maslina Darus
4
1
Department of Mathematics and Statistics, International Islamic University, 44000 Islamabad, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, 22060 Abbottabad, Pakistan
3
Department of Mathematics, Riphah International University, 44000 Islamabad, Pakistan
4
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Selangor, Malaysia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 458; https://doi.org/10.3390/math7050458
Submission received: 29 March 2019 / Revised: 11 May 2019 / Accepted: 13 May 2019 / Published: 21 May 2019
(This article belongs to the Special Issue Complex Analysis and Its Applications)
Versions Notes

Abstract

In our present investigation, we use the technique of convolution and quantum calculus to study the Salagean q-differential operator. By using this operator and the concept of the Janowski function, we define certain new classes of analytic functions. Some properties of these classes are discussed, and numerous sharp results such as coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, and integral mean inequalities of functions belonging to these classes are obtained and studied.
Keywords: analytic functions; subordination; Salagean q-differential operator analytic functions; subordination; Salagean q-differential operator

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MDPI and ACS Style

Naeem, M.; Hussain, S.; Mahmood, T.; Khan, S.; Darus, M. A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator. Mathematics 2019, 7, 458. https://doi.org/10.3390/math7050458

AMA Style

Naeem M, Hussain S, Mahmood T, Khan S, Darus M. A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator. Mathematics. 2019; 7(5):458. https://doi.org/10.3390/math7050458

Chicago/Turabian Style

Naeem, Muhammad, Saqib Hussain, Tahir Mahmood, Shahid Khan, and Maslina Darus. 2019. "A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator" Mathematics 7, no. 5: 458. https://doi.org/10.3390/math7050458

APA Style

Naeem, M., Hussain, S., Mahmood, T., Khan, S., & Darus, M. (2019). A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator. Mathematics, 7(5), 458. https://doi.org/10.3390/math7050458

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