Recurrence equations over trees in a non-Archimedean context

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11 Citations (Scopus)


In the present paper we study recurrence equations over k-ary trees. Namely, each equation is assigned to a vertex of the tree, and they are generated by contractive functions defined on an arbitrary non-Archimedean algebra. The main result of this paper states that the given equations have at most one solution. Moreover, we also provide the existence of unique solution of the equations. We should stress that the non-Archimedeanity of the algebra is essentially used, therefore, the methods applied in the present paper are not valid in the Archimedean setting.

Original languageEnglish
Pages (from-to)310-317
Number of pages8
JournalP-Adic Numbers, Ultrametric Analysis, and Applications
Issue number4
Publication statusPublished - Oct 1 2014
Externally publishedYes


  • non-Archimedean algebra
  • recurrence equation
  • tree
  • unique solution

ASJC Scopus subject areas

  • General Mathematics


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