Displaying similar documents to “On the general solution of a functional equation connected to sum form information measures on open domain. III.”

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

Palaniappan Kannappan (1980)

Stochastica

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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...

Weighted entropies

Bruce Ebanks (2010)

Open Mathematics

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We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.

On a multiplicative type sum form functional equation and its role in information theory

Prem Nath, Dhiraj Kumar Singh (2006)

Applications of Mathematics

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In this paper, we obtain all possible general solutions of the sum form functional equations ∑ i = 1 k ∑ j = 1 ℓ f ( p i q j ) = ∑ i = 1 k g ( p i ) ∑ j = 1 ℓ h ( q j ) and ∑ i = 1 k ∑ j = 1 ℓ F ( p i q j ) = ∑ i = 1 k G ( p i ) + ∑ j = 1 ℓ H ( q j ) + λ ∑ i = 1 k G ( p i ) ∑ j = 1 ℓ H ( q j ) valid for all complete probability distributions ( p 1 , ... , p k ) , ( q 1 , ... , q ℓ ) , k ≥ 3 , ℓ ≥ 3 fixed integers; λ ∈ ℝ , λ ≠ 0 and F , G , H , f , g , h are real valued mappings each having the domain I = [ 0 , 1 ] , the unit closed interval.