  Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39
and 41 are calculated in the framework of relativistic deformed mean-field
theory. The spatial components of the vector meson fields and the photon are
fully taken into account in a self-consistent manner. The calculated binding
energy differences are systematically smaller than the experimental values and
lend support to the existency of the Okamoto--Nolen-Schiffer anomaly found
decades ago in nonrelativistic calculations. For the majority of the nuclei
studied, however, the results are such that the anomaly is significantly
smaller than the one obtained within state-of-the-art nonrelativistic
calculations.
