Inner shell binding of electrons in heavy atoms is studied through the relativistic density functional theory in which many electron interactions are treated in a local density approximation. By using this theory and the Δscf procedure binding energies of several core electrons of mercury atom are calculated in the frozen and relaxed configurations. The results are compared with those carried out by the non-local Dirac-Fock Scheme.K-shell binding energies of several closed shell atoms are calculated by using the Kohn-Sham and the relativistic exchange potentials. The results are discussed and the discrepancies in our local density results, when compared with experimental values, may be attributed to the non-locality and to the many-body effects.