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Handbook of Functional Equations pp 161–208Cite as

Constructions and Extensions of Free and Controlled Additive Relations

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 95))

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.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, 4010 Debrecen, P.O.B. 12, Hungary

    Tamás Glavosits & Árpád Száz

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  1. Tamás Glavosits
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  2. Árpád Száz
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Correspondence to Tamás Glavosits .

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  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Glavosits, T., Száz, Á. (2014). Constructions and Extensions of Free and Controlled Additive Relations. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1246-9_9

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