We use of two notions functionally CONVEX (briefly, F-CONVEX) and functionally closed (briefly, F-closed) in functional analysis and obtain more results. We show that if {Aa}aÎI is a family F- CONVEX subSETs with non empty intersection of a Banach space X, then ÈaÎI Aa is F–CONVEX. Moreover, we introduce new definition of notion F-CONVEXiy.