Opuscula Math. 27, no. 2 (2007), 253-257

Opuscula Mathematica

# On the equivalence of pre-Schröder equations

Józef Kalinowski

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.

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