Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE TILTED CARATHÉODORY FUNCTION CLASS AND ITS PRACTICAL APPLICATIONS

  • Nak Eun Cho (Department of Applied Mathematics Pukyong National University) ;
  • Inhwa Kim (Anheuser-Bush School of Business Harris-Stowe State University) ;
  • Young Jae Sim (Department of Artificial Intelligence and Mathematics Kyungsung University)
  • Received : 2023.11.07
  • Accepted : 2024.01.23
  • Published : 2024.07.31
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Abstract

In this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for the tilted Carathéodory function of order β and angle α (α ∈ (-π/2, π/2) and β ∈ [0, cos α)), which maps the unit disk 𝔻 into the region {w ∈ ℂ : Re{eiαw} > β}. Using these conditions, we also derive conditions for an analytic function that maps 𝔻 into a sector defined by {w ∈ ℂ : | arg(w - γ)| < (π/2)δ}, where γ ∈ [0, 1) and δ ∈ (0, 1]. The results obtained here will be applied to find some conditions for spirallike functions and strongly starlike functions in 𝔻.

Keywords

Acknowledgement

This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2019R1I1A3A01050861).

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