On $ q $-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain

Bakhtiar Ahmad; Muhammad Ghaffar Khan; Basem Aref Frasin; Mohamed Kamal Aouf; Thabet Abdeljawad; Wali Khan Mashwani; Muhammad Arif; Bakhtiar Ahmad; Muhammad Ghaffar Khan; Basem Aref Frasin; Mohamed Kamal Aouf; Thabet Abdeljawad; Wali Khan Mashwani; Muhammad Arif

doi:10.3934/math.2021185

AIMS Mathematics

2021, Volume 6, Issue 4: 3037-3052. doi: 10.3934/math.2021185

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Research article

On $ q $-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain

1.
Abdul Wali Khan University Mardan, 23200 Mardan, Pakistan
2.
Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan
3.
Faculty of Science, Department of Mathematics, AL AL-Bayt University Mafraq, Jordon
4.
Department of Mathematics, Faculty of Science, Mansoura 35516, Egypt
5.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
6.
Department of Medical Research, China Medical University Taichung 40402, Taiwan
7.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

Received: 23 October 2020 Accepted: 08 January 2021 Published: 12 January 2021
MSC : 30C45, 30D30

Utilizing the concepts from $ q $-calculus in the field of geometric function theory, we introduce a subclass of $ p $-valent meromorphic functions relating to the domain of lemniscate of Bernoulli. The well known problem of Fekete-Szegö for this class is evaluated. Also some geometric results related to subordinations are evaluated for this class in connection with Janowski functions.
- meromorphic functions,
- $ q $-calculus,
- lemniscate of Bernoulli,
- Janowski functions
Citation: Bakhtiar Ahmad, Muhammad Ghaffar Khan, Basem Aref Frasin, Mohamed Kamal Aouf, Thabet Abdeljawad, Wali Khan Mashwani, Muhammad Arif. On $ q $-analogue of meromorphic multivalent functions in lemniscate of Bernoulli domain[J]. AIMS Mathematics, 2021, 6(4): 3037-3052. doi: 10.3934/math.2021185

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Abstract

Utilizing the concepts from $ q $-calculus in the field of geometric function theory, we introduce a subclass of $ p $-valent meromorphic functions relating to the domain of lemniscate of Bernoulli. The well known problem of Fekete-Szegö for this class is evaluated. Also some geometric results related to subordinations are evaluated for this class in connection with Janowski functions.

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