AIMS Mathematics, 2020, 5(5): 4830-4848. doi: 10.3934/math.2020308.

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New subclass of q-starlike functions associated with generalized conic domain

1 School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, Inner Mongolia, People’s Republic of China
2 Department of Mathematics, Riphah International University, 44000 Islamabad, Pakistan
3 Department of Mathematics, COMSATS University Islamabad, Abbottabad campus 22060, Pakistan
4 Mathematics and Natural Science division, Higher Colleges of Technology, Fujairah Men’s, Fujairah, United Arab Emirates

In this paper, the concepts of quantum (or q-) calculus and conic regions are combined to define a new domain Ωk,q,γ which represents the generalized conic regions. Then by using a certain generalized conic domain Ωk,q,γ we define and investigate a new subclass of normalized analytic functions in open unit disk E. We also investigate a number of useful properties and characteristics of this subclass such as, structural formula, necessary and sufficient condition, coefficient estimates, Feketo-Szego problem, distortion inequalities, closure theorem, and subordination result. We also highlight some known consequences of our main results as corollaries.
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Keywords analytic functions; quantum (or q-) calculus; q-derivative operator; q-starlike functions; conic and generalized conic domains; subordination

Citation: Xiaoli Zhang, Shahid Khan, Saqib Hussain, Huo Tang, Zahid Shareef. New subclass of q-starlike functions associated with generalized conic domain. AIMS Mathematics, 2020, 5(5): 4830-4848. doi: 10.3934/math.2020308

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