Geodesic
On the Functional Equation f phi f = f
Publications de l'Institut Mathématique, _N_S_29 (1981) no. 43, p. 61 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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In this note we determine the general solution of the equation $f\varphi f=f$, where $f:X\to Y$ is a given function and $\varphi:Y\to X$ is an unkown function ($X$ and $Y$ are arbitrary nonempty sets). The general solution of that equation is given by the formula (4), where $\varphi_0:Y\to X$ is a particular solution, $k:Y\to X$ and $h:X\to X$ are arbitrary functions, $F:X^3\times Y^3\to X$ is defined by (3). 
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     author = {Valentina Harizanov},
     title = {On the {Functional} {Equation} f phi f = f},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {61 },
     year = {1981},
     volume = {_N_S_29},
     number = {43},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1981_N_S_29_43_a8/}
}
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Valentina Harizanov. On the Functional Equation f phi f = f. Publications de l'Institut Mathématique, _N_S_29 (1981) no. 43, p. 61 . http://geodesic.mathdoc.fr/item/PIM_1981_N_S_29_43_a8/