On a class of univalent functions

Let AA be the class of analytic functions in the unit disk DD with the normalization f(0)=f′(0)−1=0f(0)=f′(0)−1=0. Denote by NN the class of functions f∈Af∈A which satisfy the condition |−z3(zf(z))‴+f′(z)(zf(z))2−1|≤1,z∈D. We show that functions in NN are univalent in DD but not necessarily starlike. Also, we present the characterization formula, necessary and sufficient coefficient conditions for functions to be in the class NN.