Abstract
The main objective of the present chapter is to prove equality (9.1.2), and to give some characterizations of the classes A, ℭ introduced in the preceding chapter. Thus we do not assume equality (9.1.2) as valid, it will be proved in the sequel1. To this aim we will need a rational version of the Hahn-Banach theorem, which we will presently prove. We start with a definition.
Theorem 10.2.2. The results of Chapter 9 (where equality (9.1.2) was postulated) will not be used in 10.1–10.2 of the present chapter, except for Theorem 9.2.8, in whose proof relation (9.1.2) was not used.
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© 2009 Birkhäuser Verlag AG
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(2009). The Classes A, B, ℭ. In: Gilányi, A. (eds) An Introduction to the Theory of Functional Equations and Inequalities. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8749-5_10
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DOI: https://doi.org/10.1007/978-3-7643-8749-5_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8748-8
Online ISBN: 978-3-7643-8749-5
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