THE TILTED CARATHÉODORY FUNCTION CLASS AND ITS PRACTICAL APPLICATIONS
THE TILTED CARATHÉODORY FUNCTION CLASS AND ITS PRACTICAL APPLICATIONS
- 대한수학회
- Bulletin of the Korean Mathematical Society
- Vol.61No.4
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2024.011121 - 1136 (16 pages)
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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{e<sup>iα</sup>w} > 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.
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