Certain subclass of analytic functions with respect to symmetric points associated with conic region

Huo Tang; Kadhavoor Ragavan Karthikeyan; Gangadharan Murugusundaramoorthy; Huo Tang; Kadhavoor Ragavan Karthikeyan; Gangadharan Murugusundaramoorthy

doi:10.3934/math.2021742

AIMS Mathematics

2021, Volume 6, Issue 11: 12863-12877. doi: 10.3934/math.2021742

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Certain subclass of analytic functions with respect to symmetric points associated with conic region

1.
School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, Inner Mongolia, China
2.
Department of Applied Mathematics and Science, National University of Science & Technology (By Merger of Caledonian College of Engineering and Oman Medical College), Sultanate of Oman
3.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, (Deemed to be University), Vellore, Tamilnadu, India

Received: 04 June 2021 Accepted: 30 August 2021 Published: 09 September 2021
MSC : 30C45, 30C80

The purpose of this paper is to introduce and study a new subclass of analytic functions with respect to symmetric points associated to a conic region impacted by Janowski functions. Also, the study has been extended to quantum calculus by replacing the ordinary derivative with a $ q $-derivative in the defined function class. Interesting results such as initial coefficients of inverse functions and Fekete-Szegö inequalities are obtained for the defined function classes. Several applications, known or new of the main results are also presented.
- analytic functions,
- Bazilevič functions,
- starlike and convex functions,
- subordination,
- Fekete-Szegö problem,
- coefficient inequalities,
- $ q $-calculus,
- Jackson's $ q $-derivative operator
Citation: Huo Tang, Kadhavoor Ragavan Karthikeyan, Gangadharan Murugusundaramoorthy. Certain subclass of analytic functions with respect to symmetric points associated with conic region[J]. AIMS Mathematics, 2021, 6(11): 12863-12877. doi: 10.3934/math.2021742

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Abstract

The purpose of this paper is to introduce and study a new subclass of analytic functions with respect to symmetric points associated to a conic region impacted by Janowski functions. Also, the study has been extended to quantum calculus by replacing the ordinary derivative with a $ q $-derivative in the defined function class. Interesting results such as initial coefficients of inverse functions and Fekete-Szegö inequalities are obtained for the defined function classes. Several applications, known or new of the main results are also presented.

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