Abstract
UDC 517.5 We introduce a new subclass of starlike functions defined as 𝒮 τ * : = { f ∈ 𝒜 : z f ' ( z ) / f ( z ) ≺ 1 + arctan z = : τ ( z ) } , where τ ( z ) maps the unit disk 𝔻 : = { z ∈ ℂ : | z | < 1 } onto a strip domain. We deduce structural formulas, as well as the growth and distortion theorems for 𝒮 τ * . In addition, inclusion relations with some well-known subclasses of 𝒮 are established and sharp radius estimates are obtained, as well as the sharp coefficient bounds for the initial five coefficients and the second and third order Hankel determinants of 𝒮 τ * .
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