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We find sharp upper bounds for $ \vert \,f^{\prime \prime }(z)/f^{\prime }(z) \vert $ such that the function f be starlike or strongly-starlike of a given order, where f is holomorphic in the unit disc U , with $ f(0)=f^{\prime }(0)-1=0 $ . These bounds are obtained by using the differential subordination technique. As a useful ingredient we obtain the radius of convexity for the function $ F(z)= z /(\exp (z)-1) $ [ABSTRACT FROM AUTHOR]