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On some functional equations from additive and nonadditive measures (III).

Palaniappan Kannappan (1980)

Stochastica

In this series, this paper is devoted to the study of two related functional equations primarily connected with weighted entropy and weighted entropy of degree beta (which are weighted additive and weighted beta additive respectively) which include as special cases Shannon's entropy, inaccuracy (additive measures) and the entropy of degree beta (nonadditive) respectively. These functional equations which arise mainly from the representation and these 'additive' properties are solved for fixed m...

On some iteration semigroups

Janusz Brzdęk (1995)

Archivum Mathematicum

Let F be a disjoint iteration semigroup of C n diffeomorphisms mapping a real open interval I onto I . It is proved that if F has a dense orbit possesing a subset of the second category with the Baire property, then F = { f t f t ( x ) = f - 1 ( f ( x ) + t ) for every x I , t R } for some C n diffeomorphism f of I onto the set of all reals R . The paper generalizes some results of J.A.Baker and G.Blanton [3].

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