Two functional equations on groups
Abstract
In this note we give the general solution of the functional equation
f(x) f(x+y) = f(y)2 f(x−y)2 g(y), x,y∈G,
and all the solutions of
f(x) f(x+y) = f(y)2 f(x−y)2 g(x) , x,y∈G,
with the additional supposition g(x) ≠ 0 for all x∈G. In both cases G denotes an arbitrary group written additively and f,g: G→ℝ are the unknown functions.
Keywords
functional equations; group; general solution
References
2. Aczél J., Some general methods in the theory of functional equations in one variable and new applications of functional equations, MTA III. Oszt. közl. 9 (1959), 375–422 (in Hungarian).
3. Aczél J., Lectures on functional equations and their application, In: Mathematics in Science and Engineering, Vol. 19, Academic Press, New York–London, 1966.
4. Ádám Zs., Lajkó K., Maksa Gy., Mészáros F., Sequenced problems for functional equations, Teach. Math. and Comp. Sci. 4(1) (2006), 179–192.
Institute of Mathematics, University of Debrecen, Hungary Hungary
Institute of Mathematics, University of Debrecen, Hungary Hungary
Institute of Mathematics, University of Debrecen, Hungary Hungary
Institute of Mathematics, University of Debrecen, Hungary Hungary
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