University of Jiroft | hasan barsam

Research

Title	Characterizations of upward and downward sets in semimodules by using topical functions
Type	Article
Keywords	Abstract concavity; b-complete; downward set; elementary topical function; extended valued function; semifield; semimodule; topical function; support set; upward set
Researchers	hasan barsam, Hossein Mohebi

Abstract

In this paper, 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 Indeed, we characterize abstract concavity and support set of this class of functions. Next, we investigate abstract concavity of extended valued topical functions f X −→ K, where K = K ∪ and = sup K Finally, as an application by using extended valued elementary topical functions, we present characterizations of upward and downward sets.