Opuscula Math. 27, no. 2 (2007), 253-257
Opuscula Mathematica
On the equivalence of pre-Schröder equations
Abstract. In the paper the equivalence of the system of two pre-Schröder functional equations (equations \((S_n)\), \((S_m)\) for \(m \gt n \geq 3\), \(n, m \in \mathbb{N}\)) and the whole system \((S)\), is considered. The results solve the problem of Gy. Targonski [Gy. Targonski, Problem P 63, Aequationes Math. 4 (1970), 251] in a particular case.
Keywords: pre-Schröder equations, Targonski's problem, torsion free semigroups.
Mathematics Subject Classification: 39B62, 39B42.
- Józef Kalinowski
- Silesian University, Department of Mathematics, ul. Bankowa 14, 40-007 Katowice, Poland
- Received: 2004-12-06.
