Acta Mathematica Scientia

, Volume 39, Issue 2, pp 369–381 | Cite as

Approximate Solution of a p-th Root Functional Equation in Non-Archimedean (2,β)-Banach Spaces

  • Iz-iddine El-FassiEmail author
  • Hamid Khodaei
  • Themistocles M. Rassias


In this paper, using the Brzdęk’s fixed point theorem [9, Theorem 1] in non-Archimedean (2,β)-Banach spaces, we prove some stability and hyperstability results for an p-th root functional equation
$$f\left( {\left( {\sum\limits_{i = 1}^k {a_i x_i^p } } \right)^{1/p} } \right) = \sum\limits_{i = 1}^k {a_i f\left( {x_i } \right)} ,$$
where p ∈ {1, ⋯, 5}, a1, ⋯, ak are fixed nonzero reals when p ∊ {1, 3, 5} and are fixed positive reals when p ∈ {2, 4}.

Key words

fixed point theorem p-th root functional equation stability non-Archimedean (2,β)-normed spaces 

2010 MR Subject Classification

39B82 47H10 65Q20 


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Iz-iddine El-Fassi
    • 1
    Email author
  • Hamid Khodaei
    • 2
  • Themistocles M. Rassias
    • 3
  1. 1.Department of Mathematics, Faculty of SciencesIbn Tofaïl UniversityKenitraMorocco
  2. 2.Department of MathematicsMalayer UniversityMalayerIran
  3. 3.Department of MathematicsNational Technical University of Athens, Zografou CampusAthensGreece

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