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A characterization of monomial functions. (English) Zbl 0895.39006

Inspired by papers of A. Dinghas, [Zur Theorie der gewöhnlichen Differentialgleichungen, Ann. Acad. Sci. Fennicae, Ser. A I 375 (1966; Zbl 0143.30602)], and of [A. Simon and P. Volkmann, Result. Math. 26, No. 3-4, 382-384 (1994; Zbl 0840.39010)] the authors give a new characterization of monomial functions.

MSC:

39B22 Functional equations for real functions
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
30C10 Polynomials and rational functions of one complex variable
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References:

[1] Aczél, J., Vorlesungen über Funktionalgleichungen und ihre Anwendungen (1961), Basel: Birkhäuser Verlag, Basel · Zbl 0096.09102
[2] Dinghas, A.,Zur Theorie der gewöhnlichen Differentialgleichungen, Ann. Acad. Sci. Fennicae, Ser. A I375 (1966). · Zbl 0143.30602
[3] Gilányi, A.,Charakterisierung von monomialen Funktionen und Lösung von Funktionalgleichungen mit Computern, Diss., Univ. Karlsruhe, 1995. · Zbl 0885.39009
[4] Kuczma, M., An introduction to the theory of functional equations and inequalities (1985), Warszawa: Panstwowe Wydawnictwo Naukowe, Universiytet Śl≸ski, Warszawa · Zbl 0555.39004
[5] Simon, A.; Volkmann, P., Eine Charakterisierung von polynomialen Funktionen mittels der Dinghasschen Intervall-Derivierten, Results in Math., 26, 382-384 (1994) · Zbl 0840.39010
[6] Volkmann, P.,Eine Charakterisierung von monomialen Funktionen n-ten Grades, n≤3, Private notes.
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