Hyers-Ulam stability of closed linear relations in Hilbert spaces
Arup Majumdar
TL;DR
This paper explores the stability of closed linear relations in Hilbert spaces, providing new characterizations and conditions for their Hyers-Ulam stability, including stability of their sums and products.
Contribution
It introduces the concept of Hyers-Ulam stability for linear relations in Hilbert spaces and establishes conditions for stability preservation under sum and product operations.
Findings
Characterization of Hyers-Ulam stability for closed linear relations
Sufficient conditions for stability of sums of relations
Conditions for stability of products of relations
Abstract
This paper introduces the concept of Hyers-Ulam stability for linear relations in normed linear spaces and presents several intriguing results that characterize the Hyers-Ulam stability of closed linear relations in Hilbert spaces. Additionally, sufficient conditions are established under which the sum and product of two Hyers-Ulam stable linear relations remain stable.
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Taxonomy
TopicsFunctional Equations Stability Results · Advanced Topics in Algebra