Single-spin asymmetries were investigated in inclusive electroproduction of charged pions and kaons from transversely polarized protons at the HERMES experiment. The asymmetries were studied as a function of the azimuthal angle ψ about the beam direction between the target-spin direction and the hadron production plane, the transverse hadron momentum relative to the direction of the incident beam, and the Feynman variable xF. The sin(ψ) amplitudes are positive for positive pions and kaons, slightly negative for negative pions and consistent with zero for negative kaons, with particular transverse-momentum but weak xF dependences. Especially large asymmetries are observed for two small subsamples of events, where also the scattered electron was recorded by the spectrometer.