We have investigated the ground-state structures of even-even Hf, W and Os isotopes within the framework of a deformed non-relativistic Hartree-Fock and a relativistic mean field formalism. A majority of the nuclei are predicted to be prolate in shape in the relativistic calculations. On the other hand, contrary to the relativistic results, we predict a shape change in a cyclic order in the non-relativistic calculations. However, in both the cases, the magnitude of the quadrupole deformation parameter agrees well with the experimental data. We also evaluated the hexadecapole deformation parameter for Hf, W and Os isotopes and irrespective of the shape change in quadrupole moments, we find a cyclic change in hexadecapole shape from positive to negative and vice versa in both the relativistic and non-relativistic formalisms.