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One functional equation with displacement in the space of continuous functions

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Abstract

In the space of continuous functions defined on a simple continuous contour, we examine the functional equationa(t)ϕ(t)+b(t)ϕ[ϕ(t)]=g(t)

A criterion for Eq. (1) being Noetherian is established under the condition that there exist a finite number of fixed points on the first multiplicity in the homeomorphism α(t) of the contour onto itself.

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Literature cited

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Authors and Affiliations

  1. Odessa State University, USSR

    V. G. Kravchenko

Authors
  1. V. G. Kravchenko
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Additional information

Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 303–311, August, 1977.

In conclusion, the author thanks G. S. Litvinchuk for guidance on the work.

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Kravchenko, V.G. One functional equation with displacement in the space of continuous functions. Mathematical Notes of the Academy of Sciences of the USSR 22, 660–665 (1977). https://doi.org/10.1007/BF01780978

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  • DOI: https://doi.org/10.1007/BF01780978

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