Applications of higher-order <i>q</i>-derivatives to the subclass of <i>q</i>-starlike functions associated with the Janowski functions

Muhammad Sabil Ur Rehman; Qazi Zahoor Ahmad; H. M. Srivastava; Nazar Khan; Maslina Darus; Bilal Khan; Muhammad Sabil Ur Rehman; Qazi Zahoor Ahmad; H. M. Srivastava; Nazar Khan; Maslina Darus; Bilal Khan

doi:10.3934/math.2021067

AIMS Mathematics

2021, Volume 6, Issue 2: 1110-1125. doi: 10.3934/math.2021067

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Applications of higher-order q-derivatives to the subclass of q-starlike functions associated with the Janowski functions

1.
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan
2.
Government Akhtar Nawaz Khan (Shaheed) Degree College KTS, Haripur 22620, Pakistan
3.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China
5.
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
6.
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
7.
School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai 200241, People's Republic of China

Received: 22 July 2020 Accepted: 15 October 2020 Published: 11 November 2020
MSC : Primary 05A30, 30C45; Secondary 11B65, 47B38

In this paper, we first investigate some subclasses of q-starlike functions. We then apply higher-order q-derivative operators to introduce and study a new subclass of q-starlike functions, which involves the Janowski functions. Several coefficient inequalities and a sufficient condition are derived. Relevant connections with a number of earlier works on this subject are also pointed out.
- multivalent functions,
- univalent functions,
- convex and q-convex functions,
- starlike and q-starlike functions,
- q-Derivative operator
Citation: Muhammad Sabil Ur Rehman, Qazi Zahoor Ahmad, H. M. Srivastava, Nazar Khan, Maslina Darus, Bilal Khan. Applications of higher-order q-derivatives to the subclass of q-starlike functions associated with the Janowski functions[J]. AIMS Mathematics, 2021, 6(2): 1110-1125. doi: 10.3934/math.2021067

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Abstract

In this paper, we first investigate some subclasses of q-starlike functions. We then apply higher-order q-derivative operators to introduce and study a new subclass of q-starlike functions, which involves the Janowski functions. Several coefficient inequalities and a sufficient condition are derived. Relevant connections with a number of earlier works on this subject are also pointed out.

References

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