Characterizations of Upward and Downward Sets in Semimodules by Using Topical Functions
Hasan Barsam, H. Mohebi · Numerical Functional Analysis and Optimization · 2016
In this article, we study topical functions f:X→K defined on a b-complete idempotent semimodule X over a b-complete idempotent semifield K with values in K. We characterize the abstract concavity and support set of this class of functions. Next, we investigate the abstract concavity of extended valued topical functions , where and ⊤: = supK. Finally, as an application, we present characterizations of upward and downward sets by using extended valued elementary topical functions.