Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ANALYTIC FUNCTIONS WITH CONIC DOMAINS ASSOCIATED WITH CERTAIN GENERALIZED q-INTEGRAL OPERATOR

  • Om P. Ahuja (Department of Mathematical Sciences Kent State University) ;
  • Asena Cetinkaya (Department of Mathematics and Computer Sciences Istanbul Kultur University) ;
  • Naveen Kumar Jain (Department of Mathematics Aryabhatta College)
  • Received : 2023.01.03
  • Accepted : 2023.04.26
  • Published : 2023.10.31
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Abstract

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

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References

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