We study the shell closure properties of the even-even neutron-deficie
nt Pt, Hg, and Pb isotopes using a deformed relativistic mean field fo
rmalism. The ground state structures are investigated by comparing the
prolate, oblate, and spherical solutions. Many of the nuclei are cons
iderably deformed in their ground state configurations. Studies of the
quadrupole and the hexadecapole moments, density distributions, and t
he single-particle level structure clearly indicate that some of the n
eutron-deficient isotopes having proton number Z = 82 do not behave as
good magic nuclei.