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

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 op...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 5; pp. 4830 - 4848
Main Authors Zhang, Xiaoli, Khan, Shahid, Hussain, Saqib, Tang, Huo, Shareef, Zahid
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
analytic functions
conic and generalized conic domains
q-derivative operator
q-starlike functions
quantum (or q-) calculus
subordination
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020308