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Open AccessArticle

Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Faculty of Computing and Information Technology, King Abdulaziz University, Rabigh 21911, Jeddah, Saudi Arabia
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 629;
Received: 11 February 2020 / Revised: 7 April 2020 / Accepted: 16 April 2020 / Published: 19 April 2020
The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q-differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters. View Full-Text
Keywords: harmonic function; Janowski starlike functions; q-derivative operator harmonic function; Janowski starlike functions; q-derivative operator
MDPI and ACS Style

Arif, M.; Barkub, O.; Srivastava, H.M.; Abdullah, S.; Khan, S.A. Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points. Mathematics 2020, 8, 629.

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