Unbounded Order Continuous Abstract Uryson Operators

TURAN B., Tülü D.

Siberian Mathematical Journal, vol.67, no.2, pp.507-516, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 2
  • Publication Date: 2026
  • Doi Number: 10.1134/s0037446626020230
  • Journal Name: Siberian Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.507-516
  • Keywords: 517.98, abstract Uryson operator, order continuous abstract Uryson operator, orthogonally additive operator, Riesz space, unbounded order continuous abstract Uryson operator
  • Gazi University Affiliated: Yes

Abstract

In this paper, we study unbounded order continuous abstract Uryson operatorsbetween Riesz spaces.We show that the space of unbounded order continuous abstract Uryson operators forms a Riesz subspace under suitable conditions.We also study several basic structural properties of such operators and analyze the relationship between order continuity andunbounded order continuity.In particular, we demonstrate that these two notions do not coincide in general and provide examples illustrating this phenomenon.