Some results on functionally convex sets in real Banach spaces

Document Type: Research Paper


1 Department of Mathematics‎, ‎Semnan University‎, ‎P‎. ‎O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran,

2 PhD student of semnan univercity

3 Department of mathematics‎, ‎Kosar University of Bojnourd‎, ‎Bojnourd‎, ‎Iran


‎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 $lbrace A_{alpha} rbrace _{alpha in I}$ 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.


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