A Subclass of q -Starlike Functions Defined by Using a Symmetric q -Derivative Operator and Related with Generalized Symmetric Conic Domains

Shahid Khan, Saqib Hussain, Muhammad Naeem, Maslina Darus and Akhter Rasheed
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Shahid Khan: Department of Mathematics, Riphah International University, Islamabad 44000, Pakistan
Saqib Hussain: Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22010, Pakistan
Muhammad Naeem: Department of Mathematics and Statistic, International Islamic University, Islamabad 44000, Pakistan
Maslina Darus: Department of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia
Akhter Rasheed: Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22010, Pakistan

Mathematics, 2021, vol. 9, issue 9, 1-12

Abstract: In this paper, the concepts of symmetric q -calculus and conic regions are used to define a new domain Ω k , q , α ˜ , which generalizes the symmetric conic domains. By using the domain Ω k , q , α ˜ , we define a new subclass of analytic and q -starlike functions in the open unit disk U and establish some new results for functions of this class. We also investigate a number of useful properties and characteristics of this subclass, such as coefficients estimates, structural formulas, distortion inequalities, necessary and sufficient conditions, closure and subordination results. The proposed approach is also compared with some existing methods to show the reliability and effectiveness of the proposed methods.

Keywords: quantum (or q-)calculus; symmetric q-derivative operator; conic domain; generalized symmetric conic domain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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