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

Xiaoli Zhang Shahid Khan Saqib Hussain Huo Tang Zahid Shareef

*Corresponding author: Huo Tang thth2009@163.com

Math2020,5,4830doi:10.3934/math.2020308

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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