Characterizations of Upward and Downward Sets in Semimodules by Using Topical Functions. (1st November 2016)

• Record Type: Journal Article
• Authors: Barsam, H.; Mohebi, H.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 11(2016)
• Page Start: 1354
• Page End: 1377
• Publication Date: 2016-11-01
• Subjects: Abstract concavity; b-complete; downward set; elementary topical function; extended valued function; semifield; semimodule; topical function; support set; upward set; 06F07 -- 26A48 -- 26B25 -- 52A01 -- 06F20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1193518
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: 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 ⊤: = sup K . Finally, as an application, we present characterizations of upward and downward sets by using extended valued elementary topical functions.