ISSN:
1420-8903
Keywords:
39B50
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary In 1970, Halina Swiatak considered the functional equation $$\begin{gathered} f(xyz) + f(xyz^{ - 1} ) + f(xy^{ - 1} z) + f(x^{ - 1} yz) \hfill \\ = 4\{ f(x) + f(y) + f(z)\} + 2\{ g(x)g(y) + g(y)g(z) + g(x)g(z)\} , \hfill \\ \end{gathered} $$ wheref andg are functions defined on an arbitrary abelian group and taking values in an arbitrary commutative ring without proper zero divisors. She determined the general solution in the caseg(e) ≠ 0, wheree is the unit element of the group, and asked what the general solution is. In this paper, we determine the general solution of the above equation and some related functional equations. Further, we do not assume the group to be abelian but we assume thatf satisfies the Kannappan condition.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01855883
Permalink