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Article

A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives

1
School of Mathematical Sciences, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China
2
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
5
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22010, Pakistan
6
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1470; https://doi.org/10.3390/math8091470
Received: 20 July 2020 / Revised: 15 August 2020 / Accepted: 21 August 2020 / Published: 1 September 2020
In the present investigation, by using certain higher-order q-derivatives, the authors introduce and investigate several new subclasses of the family of multivalent q-starlike functions in the open unit disk. For each of these newly-defined function classes, several interesting properties and characteristics are systematically derived. These properties and characteristics include (for example) distortion theorems and radius problems. A number of coefficient inequalities and a sufficient condition for functions belonging to the subclasses studied here are also discussed. Relevant connections of the various results presented in this investigation with those in earlier works on this subject are also pointed out. View Full-Text
Keywords: multivalent functions; q-difference (or q-derivative) operator; distortion theorems; radius problem multivalent functions; q-difference (or q-derivative) operator; distortion theorems; radius problem
MDPI and ACS Style

Khan, B.; Liu, Z.-G.; Srivastava, H.M.; Khan, N.; Darus, M.; Tahir, M. A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives. Mathematics 2020, 8, 1470. https://doi.org/10.3390/math8091470

AMA Style

Khan B, Liu Z-G, Srivastava HM, Khan N, Darus M, Tahir M. A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives. Mathematics. 2020; 8(9):1470. https://doi.org/10.3390/math8091470

Chicago/Turabian Style

Khan, Bilal, Zhi-Guo Liu, Hari M. Srivastava, Nazar Khan, Maslina Darus, and Muhammad Tahir. 2020. "A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives" Mathematics 8, no. 9: 1470. https://doi.org/10.3390/math8091470

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