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3 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

3 Domańska K.

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On associative rational functions with multiplicative generators

Domańska K.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2015

Vol. 20

31--38

We consider the class of rational functions defined by the formula F(x, y) = φˉ¹(φ(x)φ(y)), where φ is a homographic function and we describe associative functions of the above form.

On associative rational functions with additive generators

Domańska K.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2013

Vol. 18

7--10

We consider the class of rational functions defined by the formula F(x, y) = ϕ −1 (ϕ(x) + ϕ(y)), where ϕ is a homographic function and we describe all associative functions of the above form.

On some addition formulas for homographic type functions

Domańska K.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2012

Vol. 17

17-24

We deal with the functional equation (so called addition formula) of the form f(x + y) = F(f(x),f(y)), where F is an associative rational function. The class of associative rational functions was described by A. Chéritat [1] and his work was followed by a paper of the author. For function F deﬁned by F(x,y) = ϕ−1(ϕ(x) + ϕ(y)), where ϕ is a homographic function, the addition formula is fulﬁlled by homographic type functions. We consider the class of the associative rational functions defined by formula F(u,v) =uv αuv + u + v, where α is a ﬁxed real numer.