Invariance of means
نویسندگان
چکیده
منابع مشابه
On the Inversion Invariance of Invariant Means
An invariant mean on a group G is a normalized, positive, translation invariant linear functional defined on the space of all bounded complex valued functions on G. Some groups possess an invariant mean (or are said to be amenable), while others do not. In particular, all abelian groups are amenable [2, §17.5]. An invariant mean on a group need not be inversion invariant. It is quite easy to sh...
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We solve the so-called invariance equation in the class of Heinz means, that is, we give necessary and sufficient conditions for the constants 0 p,q,r 1 such that the identity Hp(Hq(x,y),Hr(x,y)) = Hp(x,y) (x,y ∈ R+) holds true where the Heinz mean Hp is defined for 0 p 1 as Hp(x,y) = xpy1−p + x1−pyp 2 . The Taylor expansion of the Heinz mean is used. Mathematics subject classification (2010): ...
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2018
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-018-0564-5