To lowest order of perturbation theory we show that an equivalence can be established between a PT -symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent mass Hamiltonian h. An important feature of h is that it reveals a domain of couplings where the quartic potential could be attractive, vanishing or repulsive. We also determine the associated physical quantities. © Institute of Physics, Academy of Sciences of Czech Republic 2006.