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On alternative functional equations. (English) Zbl 0348.39010

MSC:

39B52 Functional equations for functions with more general domains and/or ranges

References:

[1] J. Aczél, K. Fladt, andM. Hosszú,Lössungen einer mit dem Doppelverhältnis zusammenhängender Funktionalgleichung. Magyan Tud. Akad. Mat. Kutatö Int. Közl.7 (1972), 335–352.
[2] P. Fischer andGy. Muszély,A Cauchy-féle függvényegyenlet bizonyos típusú általánosításai. Mat. Lapok16 (1965), 67–75.
[3] M. Hosszú,Egy alternativ függvényegyenletröl. Mat. Lapok14 (1963), 98–102.
[4] M. Hosszú andH. Światak,Remarks on the functional equation e(x, y)f(xy)=f(x)+f(y). Publ. Techn. Univ. Miskolc30 (1970), 323–325.
[5] H. Światak,On the equation (x + y) 2 =[(x)g(y)+(y)g(x)] 2. Zeszyty Nauk. Univ. Jagiello. Prac Mat.10 (1965), 97–104. · Zbl 0282.39006
[6] –,On the functional equations \(f_1 (x_1 + \cdot \cdot \cdot + x_n )^2 = [\sum _{(i_{1, \cdot \cdot \cdot ,} i_n )} f_1 (x_{i_1 } ) \cdot \cdot \cdot f_n (x_{i_n } )]^2 \) . Ann. Univ. Sci. Budapest Eötvös Sect. Math.10 (1967), 49–52. · Zbl 0155.46502
[7] –,On some symmetrical equations of the form \(f_1 (x_1 + \cdot \cdot \cdot + x_n ) = \sum _{(i_1 , \cdot \cdot \cdot ,i_n )} f_1 (x_{i_2 } ) \cdot \cdot \cdot f_n (x_{i_n } )\) . Ann. Polon. Math.19 (1967), 271–286. · Zbl 0158.15301
[8] –,On the equivalence of some functional equations. Publ. Techn. Univ. Miskolc30 (1970), 275–279. · Zbl 0198.02802
[9] –,On the functional equation f(x + y) 2=[f(x)+f(y)] 2. Publ. Techn. Univ. Miskolc30 (1970), 307–308.
[10] E. Vincze,Alternativ függvényegyenletek megoldásairol. Mat. Lapok15 (1964), 179–195.
[11] –,Beitrag zur theorie der Cauchyschen Funktionalgleichungen. Arch. Math. (Basel)15 (1964), 132–135. · Zbl 0137.32702
[12] –,Über eine Vera lgemeinerung der Cauchyschen Funktionalgleichung. Funkcial Ekvac.6 (1964), 55–64.
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