Some results on functionally convex sets in real Banach spaces

Document Type : Research Paper

Authors

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

Abstract

‎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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References

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[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.
Wavelet and Linear Algebra
Volume 3, Issue 1
spring and summer
2016
Pages 61-67

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