SEPARATION THEOREM WITH RESPECT TO SUB-TOPICAL FUNCTIONS AND ABSTRACT CONVEXITY
- Department of Mathematics, University of Mazandaran, Babolsar 47416 − 1468, Iran..
- Islamic Azad University, Ayatollah Amoli branch, Amol, Iran.
This paper deals with topical and sub-topical functions in a class
of ordered Banach spaces. The separation theorem for downward sets and
sub-topical functions is given. It is established some best approximation problems
by sub-topical functions and we will characterize sub-topical functions as
superimum of elementary sub-topical functions.
- Downward set
- Subdifferential set
- ordered Banach space
- topical function
- sub-topical function
- separation theorem
- abstract convex set.
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