### 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.

Original language | English |
---|---|

Article number | 458 |

Journal | Mathematics |

Volume | 7 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

### Fingerprint

### Keywords

- Analytic functions
- Salagean q-differential operator
- Subordination

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematics*,

*7*(5), [458]. https://doi.org/10.3390/math7050458

**A new subclass of analytic functions defined by using Salagean q-differential operator.** / Naeem, Muhammad; Hussain, Saqib; Mahmood, Tahir; Khan, Shahid; Darus, Maslina.

Research output: Contribution to journal › Article

*Mathematics*, vol. 7, no. 5, 458. https://doi.org/10.3390/math7050458

}

TY - JOUR

T1 - A new subclass of analytic functions defined by using Salagean q-differential operator

AU - Naeem, Muhammad

AU - Hussain, Saqib

AU - Mahmood, Tahir

AU - Khan, Shahid

AU - Darus, Maslina

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Analytic functions

KW - Salagean q-differential operator

KW - Subordination

UR - http://www.scopus.com/inward/record.url?scp=85067828170&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067828170&partnerID=8YFLogxK

U2 - 10.3390/math7050458

DO - 10.3390/math7050458

M3 - Article

AN - SCOPUS:85067828170

VL - 7

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 5

M1 - 458

ER -