Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19363120160601Some results on functionally convex sets in real Banach spaces616719956ENMadjidEshaghiDepartment of Mathematics‎, ‎Semnan University‎, ‎P‎. ‎O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran,HamidrezaReisiPhD student of semnan univercityAlirezaMoazzenDepartment of mathematics‎, ‎Kosar University of Bojnourd‎, ‎Bojnourd‎, ‎IranJournal Article20160201We 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 $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$, then $bigcup_{alphain I}A_{alpha}$ is F--convex. Moreover, we introduce new definition of notion F--convexiy.https://wala.vru.ac.ir/article_19956_c84c54eb7ec49c507aa1fd6074db65fe.pdf