Applications of a differential operator to a class of harmonic mappings defined by Mittag-leffer functions

Muhammad Ghaffar Khan; Bakhtiar Ahmad; Thabet Abdeljawad; Muhammad Ghaffar Khan; Bakhtiar Ahmad; Thabet Abdeljawad

doi:10.3934/math.2020436

AIMS Mathematics

2020, Volume 5, Issue 6: 6782-6799. doi: 10.3934/math.2020436

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Research article

Applications of a differential operator to a class of harmonic mappings defined by Mittag-leffer functions

1.
Department of Mathematics, Abdul Wali Khan University Mardan, 23200 Mardan, Pakistan
2.
Department of Mathematics, Govt. Degree College Mardan, 23200 Mardan, Pakistan
3.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
4.
Department of Medical research, China Medical University Taiwan, Taichung, Taiwan
5.
Department of Computer Science and information Engineering, Asia University, Taichung, Taiwan

Received: 02 April 2020 Accepted: 26 August 2020 Published: 02 September 2020
MSC : 30C45, 30C50

Utilizing the concepts of Harmonic analysis and Mittag-Leffler functions we introduce a new subclass of harmonic mappings involving differential operator in domain of Janowski functions. Moreover, we investigate analytic criteria, necessary and sufficient conditions, topological properties, extreme points, radii problems and some applications of this work for the class of functions defined by this operator.
- harmonic functions,
- Janowski function,
- starlike functions,
- Mittag-Leffer Functions,
- radii problems
Citation: Muhammad Ghaffar Khan, Bakhtiar Ahmad, Thabet Abdeljawad. Applications of a differential operator to a class of harmonic mappings defined by Mittag-leffer functions[J]. AIMS Mathematics, 2020, 5(6): 6782-6799. doi: 10.3934/math.2020436

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Abstract

Utilizing the concepts of Harmonic analysis and Mittag-Leffler functions we introduce a new subclass of harmonic mappings involving differential operator in domain of Janowski functions. Moreover, we investigate analytic criteria, necessary and sufficient conditions, topological properties, extreme points, radii problems and some applications of this work for the class of functions defined by this operator.

References

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