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We use the GALEX data of the GUViCS survey to construct the NUV luminosityfunction of the Virgo cluster over ~ 300 deg.2, an area covering the clusterand its surrounding regions up to ~ 1.8 virial radii. The NUV luminosityfunction is also determined for galaxies of different morphological type andNUV-i colour, and for the different substructures within the cluster. Theseluminosity functions are robust vs. statistical corrections since based on asample of 833 galaxies mainly identified as cluster members with spectroscopicredshift (808) or high-quality optical scaling relations (10). We fit theseluminosity functions with a Schechter function, and compare the fittedparameters with those determined for other nearby clusters and for the field.The faint end slope of the Virgo NUV luminosity function (alpha = -1.19), heresampled down to ~ NUV = -11.5 mag, is significantly flatter than the onemeasured in other nearby clusters and similar to the field one. Similarly M* =-17.56 is one-to-two magnitudes fainter than measured in Coma, A1367, theShapley supercluster, and the field. These differences seem due to the quiteuncertain statistical corrections and the small range in absolute magnitudesampled in these clusters. We do not observe strong systematic differences inthe overall NUV luminosity function of the core of the cluster with respect tothat of its periphery. We notice, however, that the relative contribution ofred-to-blue galaxies at the faint end is inverted, with red quiescent objectsdominating the core of the cluster and star forming galaxies dominating beyondone virial radius. These observational evidences are discussed in the frameworkof galaxy evolution in dense environments.

The GALEX Ultraviolet Virgo Cluster Survey (GUViCS). VI: The UV luminosity function of the Virgo cluster and its surrounding regions