On Steiner loops and power associativity.
On some functional equations from additive and nonadditive measures (III).
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...
Espacios de producto interno (II).
Among normal linear spaces, the inner product spaces (i.p.s.) are particularly interesting. Many characterizations of i.p.s. among linear spaces are known using various functional equations. Three functional equations characterizations of i.p.s. are based on the Frchet condition, the Jordan and von Neumann identity and the Ptolemaic inequality respectively. The object of this paper is to solve generalizations of these functional equations.
On a generalization of sum form functional equation (I).
The Shannon entropy has the sum form ∑f(p) with f(x) = -x logx (x belonging to [0,1]). This together with the property of additivity leads to the 'sum' functional equation...
On a multiplace functional equation related to information measures and functions
On some functional equations from additive and nonadditive measures. IV.
On a functional equation connected to sum form nonadditive information measures on an open domain (III).
This is a part of a recent program by a number of authors to study information measures on open domain. In this series, this paper is devoted to the study of the functional equation (2) on an open domain. This functional equation is connected to the weighted entropy and weighted entropy of degree a.
On a generalized directed-divergence function
Generalization of sum representation functional equations. II: Generalized directed divergence
On a functional equation connected to sum form nonadditive information measures on an open domain. I.
An axiomatic characterization of generalized directed-divergence
Page 1