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

Muhammad Arif, Omar Barkub, Hari Mohan Srivastava, Saleem Abdullah and Sher Afzal Khan
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Muhammad Arif: Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Omar Barkub: Faculty of Computing and Information Technology, King Abdulaziz University, Rabigh 21911, Jeddah, Saudi Arabia
Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Saleem Abdullah: Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Sher Afzal Khan: Faculty of Physical and Numerical Sciences, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan

Mathematics, 2020, vol. 8, issue 4, 1-16

Abstract: 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.

Keywords: harmonic function; Janowski starlike functions; q-derivative operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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