General form of $$$(\lambda,\varphi)$$$-additive operators on spaces of $$$L$$$-space-valued functions

V.F. Babenko; V.V. Babenko; O.V. Kovalenko; N.V. Parfinovych

doi:10.15421/242201

General form of $$$(\lambda,\varphi)$$$-additive operators on spaces of $$$L$$$-space-valued functions

V.F. Babenko (Oles Honchar Dnipro National University), https://orcid.org/0000-0001-6677-1914
V.V. Babenko (Drake University), https://orcid.org/0000-0003-4859-4437
O.V. Kovalenko (Oles Honchar Dnipro National University), https://orcid.org/0000-0002-0446-1125
N.V. Parfinovych (Oles Honchar Dnipro National University), https://orcid.org/0000-0002-3448-3798

Abstract

The goal of the article is to characterize continuous $$$(\lambda,\varphi)$$$-additive operators acting on measurable bounded functions with values in $$$L$$$-spaces. As an application, we prove a sharp Ostrowski type inequality for such operators.

Keywords

$$$L$$$-space; $$$(\lambda,\varphi)$$$-additive operator

MSC 2020

41A65; 26D10; 46E40; 41A44

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References

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