Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON FUNCTIONS STARLIKE WITH RESPECT TO n-PLY SYMMETRIC, CONJUGATE AND SYMMETRIC CONJUGATE POINTS

  • Received : 2021.10.01
  • Accepted : 2022.02.22
  • Published : 2022.10.01
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Abstract

For given non-negative real numbers 𝛼k with ∑mk=1 𝛼k = 1 and normalized analytic functions fk, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑mk=1 𝛼kfk(z), and Fn(z) := n-1 ∑n-1j=0 e-2j𝜋i/nF(e2j𝜋i/nz). This paper studies the functions fk satisfying the subordination zf'k(z)/Fn(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

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Acknowledgement

The authors are thankful to the referee for the comments to improve the readability of the paper.

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