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Letf(z)=z+a₂z²+a₃z³+··· be a normalized strongly close-to-convex function of order α>0 defined on the unit disk D . This means that there is a normalized convex univalent function ϕ and β∈ R such that[formula]forz∈ D . Then|a ₃−a ₂²|+ 1 3 |a _x| ²≤ 1 3 (1+4α+2α ²) and|a ₃− 2 3 a ₂²+ 2 3 |a ₂| ²≤ 1 3 (3+4α+2α ²) with equality if and only iffis a rotation of[formula]