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In this paper we present the star formation properties of$\rm{I_{subaru}\leq}$ 23 X-ray detected AGN and non-AGN galaxies in the greenvalley with far-IR (FIR) emission, using data from the COSMOS field. Wemeasured star formation rates (SFR) using FIR Herschel/PACS data and weobserved the location of AGN and non-AGN galaxies on the main-sequence of starformation. We went a step further in analysing the importance of AGN inquenching star formation in the green valley, the region proposed to be thetransitional phase in galaxy evolution where galaxies are moving from later- toearlier-types. We found that most of our green valley X-ray detected AGN withfar-IR emission have SFRs higher than the ones of inactive galaxies at fixedstellar mass ranges, the result that is different when considering opticaldata. These FIR AGN have still very active star formation, being located eitheron or above the main-sequence of star formation (in total 82\% of our sample).Therefore, they do not show signs of star formation quenching, but rather itsenhancement. Our results may suggest that for X-ray detected AGN with FIRemission if there is an influence of AGN feedback on the star formation in thegreen valley the scenario of AGN positive feedback seem to take place, ratherthan the negative one.

Star formation of far-IR AGN and non-AGN galaxies in the green valley: possible implication of AGN positive feedback