Constructions and Extensions of Free and Controlled Additive Relations

Tamás Glavosits () and Árpád Száz ()
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Tamás Glavosits: University of Debrecen
Árpád Száz: University of Debrecen

A chapter in Handbook of Functional Equations, 2014, pp 161-208 from Springer

Abstract: Abstract By using several auxiliary results on relations and their intersection convolutions, we give some necessary and sufficient conditions in order that a certain additive partial selection relation Φ of a relation F of one group X to another Y could be extended to a total, additive selection relation Ψ of the relation $F+\Phi(0)$ . The results obtained extend some Hahn–Banach type extension theorems of B. Rodríguez-Salinas, L. Bou, Z. Gajda, A. Smajdor, W. Smajdor, and the second author. Moreover, they can be used to prove some alternate forms of the Hyers–Ulam type selection theorems of Z. Gajda, R. Ger, R. Badora, Zs. Páles, and the second author.

Keywords: Additive and homogeneous relations; Intersection convolutions of relations; Extensions of additive partial selection relations (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_9

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DOI: 10.1007/978-1-4939-1246-9_9

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