Showing papers by "Prasanna K. Sahoo published in 1995"
TL;DR: In this paper, the main goal is to determine the general solution of the functional equation fl (Xy) + f2(xy'-1) = f3(x)+ f4(y + f5(x), f6(Y), fi(txy) = fi(tyx) (i = 1, 2) where fi are complex-valued functions defined on a group.
Abstract: Our main goal is to determine the general solution of the functional equation fl (Xy) + f2(xy'-1) = f3(x) + f4(y) + f5(x) f6(Y), fi(txy) = fi(tyx) (i = 1, 2) where fi are complex-valued functions defined on a group This equation contains, among others, an equation of H Swiatak whose general solution was not known until now and an equation studied by KS Lau in connection with a characterization of Rao's quadratic entropies Special cases of this equation also include the Pexider, quadratic, d'Alembert and Wilson equations
29 citations
8 citations
TL;DR: It is shown that the additive k-dimensional information measures along with the sum property are essentially the linear combination of the Shannon entropies and Kerridge inaccuracies.
3 citations
TL;DR: In this article, the authors present stated unsolved problems dealing with notions ordinarEhy encountered in undergraduate mathematics, accompanied by relevant references (if any are known to the author) and by a brief descraption of known partial or related results.
Abstract: In this department the MONTHLY presents easiffiy stated unsolved problems dealing with notions ordinarEhy encountered in undergraduate mathematics. Each problem should be accompanied by relevant references (if any are known to the author) and by a brief descraption of known partial or related results. Typescrapts should be sent to Richard Guy, Department of Mathematacs & Statistacs, The Universaty of Calgary, Alberta, Canada T2N 1N4.
3 citations
01 Aug 1995
TL;DR: For distinct points x 1,x2,x 2,x 3,x 4,x 5,x 6,x 7,x 8,x 9,x 10,x 11,x 12,x 13,x 14,x 15,x 16,x 17,x 18,x 19,x 20,x 21,x 22,x 23,x 24,x 25,x 26,x 27,x 28,x 29,x 30,x 31,x 32,x 33,x 34,x 35,x 36,x
Abstract: For distinct points x1,x2,…,xn in ℛ (the reals), letϕ[x1, x2,…,xn] denote the divided difference ofϕ. In this paper, we determine the general solutionϕ,g: ℛ → ℛ of the functional equationϕ[x1,x2,…,xn] =g(x1,+ x2 + … + xn) for distinct x1,x2,…, xn in ℛ without any regularity assumptions on the unknown functions.
2 citations