We consider the class of univalent functions f(z) = z+a_3z^3+a_4z^4+・・・ analytic in the unit disc and satisfying |(z^ 2f’(z)/f^2(z))−1| < 1, and show that such functions are starlike if they satisfy |(z^2f’ (z)/f^2(z))−1| < (1/√2).
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