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A characterization of monomial functions

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Summary

The aim of this paper is to give a characterization of monomial functions with the aid of an operator\(\tilde D\) introduced in Section 1. The present results were inspired by A. Dinghas [2] and A. Simon and P. Volkmann [5], who treated the characterization of polynomial functions by the so called Dinghas interval-derivatives.

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References

  1. Aczél, J.,Vorlesungen über Funktionalgleichungen und ihre Anwendungen, Birkhäuser Verlag, Basel, 1961.

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  2. Dinghas, A.,Zur Theorie der gewöhnlichen Differentialgleichungen, Ann. Acad. Sci. Fennicae, Ser. A I375 (1966).

  3. Gilányi, A.,Charakterisierung von monomialen Funktionen und Lösung von Funktionalgleichungen mit Computern, Diss., Univ. Karlsruhe, 1995.

  4. Kuczma, M.,An introduction to the theory of functional equations and inequalities, Panstwowe Wydawnictwo Naukowe, Universiytet Śl≸ski, Warszawa, 1985.

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  5. Simon, A. andVolkmann, P.,Eine Charakterisierung von polynomialen Funktionen mittels der Dinghasschen Intervall-Derivierten, Results in Math.26 (1994), 382–384.

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  6. Volkmann, P.,Eine Charakterisierung von monomialen Funktionen n-ten Grades, n≤3, Private notes.

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Correspondence to Attila Gilányi.

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Gilányi, A. A characterization of monomial functions. Aequ. Math. 54, 289–307 (1997). https://doi.org/10.1007/BF02755461

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  • DOI: https://doi.org/10.1007/BF02755461

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