Generalizations. The Method of Invariant Means
As was seen above in Corollary 1.2, there is no difficulty in generalizing Theorem 1.1 to mappings from a commutative semigroup S to a Banach space. We note here that the property of commutativity was used only in demonstrating the additivity of the mapping g.
KeywordsBanach Space Functional Equation Additive Function Banach Lattice Topological Vector Space
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