Palaniappan Kannappan

Functional equations and inequalities with applications

Basic Equations: Cauchy and Pexider Equations.- Matrix Equations.- Trigonometric Functional Equations.- Quadratic Functional Equations.- Characterization of Inner Product Spaces.- Stability.- Characterization of Polynomials.- Nondifferentiable Functions.- Characterization of Groups, Loops, and Closure Conditions.- Functional Equations from Information Theory.- Abel Equations and Generalizations.- Regularity Conditions-Christensen Measurability.- Difference Equations.- Characterization of Special Functions.- Miscellaneous Equations.- General Inequalities.- Applications.

A directed-divergence function of type β*

A new concept of directed-divergence function of type β is introduced in this paper. This concept is used in obtaining a directed-divergence of type β which generalizes Kullbacks directed-divergence and has a relation with REnyis information-gain of order β . This relation can be used to give another characterization of information-gain of order β . A characterization theorem for the directed-divergence of type β is proved with the help of a functional equation.

A mixed theory of information. III. Inset entropies of degree β

In generalization of a purely probabilistic result ( Daroczy, 1970 , Information and Control 16 , 36–41), the general form of. symmetric, β -recursive entropies of randomized systems of events is determined in the framework of the mixed theory of information.

On a characterization of directed divergence

Shannons entropy was characterized by many authors by assuming different sets of postulates. One other measure associated with Shannons entropy is directed divergence or information gain. In this paper, a characterization theorem for the measure directed divergence is given by assuming intuitively reasonable postulates and with the help of functional equations.

Characterizations of sum form information measures on open domains

SummaryThe goal of this paper is to give a survey of all important characterizations of sum form information measures that depend uponk discrete complete probability distributions (without zero probabilities) of lengthn and which satisfy a generalized additivity property. It turns out that most of the problems have been solved, but some open problems lead to the very simple looking functional equations

Klee's Trigonometry Problem

f(pq) + f(p(1 - q)) + f((1 - p)q) - f((1 - p)(1 - q)) = 0, p,q \in ]0, 1[^k (FE)

Characterization of Inner Product Spaces

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