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— Darôczy [1] generalized the functional équation given by Kendall [4] as ƒ(*) + (i xf and introduced the concept of information functions of type-§ which are the solutions of the functional équation (0.1) under suitable boundary conditions. Authors [9] have formed the functional équation of two variables (0.2) is a generalization of KendalVs functional équation in two variables. The solutions of (0.2) are inaccuracy functions under the conditions f(Q; 0) =*/(l; 1);/(1/2; 1/2) = 1. (0.3) i/i /Aw paper we have generalized the functional équation (0.2) by introducing two para* meters 3 and y such that 3, y > 0 a»*/ 3 ^ 1 w/te« y ~ 1 as f(xi; yô + (1 — . 0 —AT2 1 — yzj (0.4) équation is a generalization of Darôczy équation (0.1) in more than one way because it is a functional équation in two variables and involves two parameters 0 and y. The solutions of this functional équation under boundary conditions (0.3) are defined as the inaccuracy functions of type (p, Y). These inaccuracy functions of type (3, y) give rise to new measure of inaccuracy H^^(P ; Q) of type (3, Y). Also when y = 1 and 3 -> 1 then (0.4) is same as n (0.2). Some properties ofH®*"ù(P; Q) are studied. * Author is grateful to C.S.I.R. (India) for financial assistance. (1) Faculty of Mathematics, University of Delhi (India). Revue Française d'Automatique, Informatique et Recherche Opérationnelle n° déc. 1972, R-3. 86 B. D. SHARMA ET R. AUTAR

Generalized functional equation of two variables in information theory