<p>Sub-Doppler fluorescence resonances at the central frequencies of atomic (molecular) transitions induced by stationary broadband optical pumping in a cylindrical cell with a rarefied gas medium are established and analyzed. The pump radiation is considered to propagate transversely through a relatively narrow region of this cell. The dependences of the established sub-Doppler resonances on the intensity and spatial distribution of such an optical pumping are analyzed. The proposed method of high-resolution spectroscopy allows one to reduce the Doppler broadening of the recorded fluorescence resonances by a value equal to the ratio of the gas-cell diameter to the relatively narrow width of the local region of the pumping radiation.</p>