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001-es BibID:BIBFORM076808
035-os BibID:(Wos)000451657400016 (Scopus)85054567704
Első szerző:Olbryś, Andrzej (matematikus)
Cím:Support theorems in abstract settings / Andrzej Olbrys, Zsolt Páles
Dátum:2018
ISSN:0033-3883 2064-2849
Megjegyzések:In this paper, we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain space, we allow algebraic structures equipped with families of algebraic operations whose operations are mutually distributive with respect to each other. We introduce several new concepts in such algebraic structures, the notions of convex set, extreme set, and interior point with respect to a given family of operations, furthermore, we describe their most basic and required properties. In the context of the range space, we introduce the notion of completeness of a partially ordered set with respect to the existence of the infimum of lower bounded chains, we also offer several sufficient conditions which imply this property. For instance, the order generated by a sharp cone in a vector space turns out to possess this completeness property. By taking several particular cases, we deduce support and extension theorems in various classical and important settings.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény hazai lapban
folyóiratcikk
Megjelenés:Publicationes Mathematicae Debrecen. - 93 : 1-2 (2018), p. 215-240. -
További szerzők:Páles Zsolt (1956-) (matematikus)
Pályázati támogatás:OTKA K-111651
OTKA
EFOP-3.6.1-16-2016-00022
EFOP
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