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- W257415149 abstract "In the present paper we find a linear operator on a function space, essentially larger than the space of all bounded functions on an amenable semigroup, which behaves like an invariant mean. This leads to an extension of the Hyers-Ulam stability theorem for Cauchy's functional equation in the case of vector-valued mappings defined on amenable semigroups. 1. Introduction. This paper is a continuation of our study which we carried out in (1) and (2) . We shall formulate all our results in the left invariant version. It is quite obvious how to rephrase the theorems so as to obtain their right invariant analogues. The proofs of these alternative theorems require only minor changes, therefore, may also be omitted. Let Y be a real linear space and let C be a non-empty class of subsets of Y. We say that the family C has the binary intersection property if every subfamily of C any two members of which intersect has a non-empty inter section. Moreover, a collection C is termed the linear invariant family if and only if C is invariant with respect to translations by vectors of Y, i.e." @default.
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- W257415149 date "1994-01-01" @default.
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- W257415149 title "ON APPROXIMATELY ADDITIVE FUNCTIONS" @default.
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