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.


[1] D. Aliprantis and C. Border, Infinite Dimensional Analysis, 2th. edition. Springer, 1999.
[2] J. B. Conway. A Course in Functionall Analysis, Springer-verlag, 1985.
[3] N. Dunford and J. T. Schwartz, Linear operators. Part 1, Interscience, New York 1958.
[4] E. Zeidler. Nonlinear Functional Analysis and its Applications I: Fixed Point Theorems, Springer-Verlog New
York, 1986.
[5] M. Eshaghi, H. Reisi Dezaki and A. Moazzen, Functionally convex sets and functionally closed sets in real
Banach spaces, Int. J. Nonlinear Anal. Appl., 7(1)(2016), 289–294.