Invariant Translative Mappings and a Functional Equation

H. Izumi, J. Matkowski

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Let K, M, N: ℝ2 → ℝ be translative functions. Then K is invariant with respect to the mapping (M,N): ℝ2 → ℝ2 if and only if the functions h = K(·, 0), f = M (·, 0), g = N(·, 0) satisfy the functional equation h(x) = h(f(x) - g(x)) + g(x), x ∈ ℝ. If K, M, N are means, then h(0) = f(0) = g(0) = 0. The formal power solutions and analytic solutions of this functional equation, satisfying these initial conditions, are considered.

Original languageEnglish
Pages (from-to)220-231
Number of pages12
JournalActa Mathematica Hungarica
Issue number1
Publication statusPublished - 2014 Jun
Externally publishedYes


  • 39B22
  • 39B32
  • analytic function
  • entire function
  • formal powers series
  • functional equation
  • invariant mean
  • mean
  • primary 30D05
  • secondary 26E60

ASJC Scopus subject areas

  • Mathematics(all)


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