### AIMS Mathematics

2020, Issue 5: 4830-4848. doi: 10.3934/math.2020308
Research article

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

• Received: 27 February 2020 Accepted: 20 May 2020 Published: 02 June 2020
• MSC : 30C45, 30C50

• 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.

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

### Related Papers:

• 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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