数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 369-381.doi: 10.1007/s10473-019-0203-9

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APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES

Iz-iddine EL-FASSI1, Hamid KHODAEI2, Themistocles M. RASSIAS3   

  1. 1. Department of Mathematics, Faculty of Sciences, Ibn Tofaïl University, B. P. 133, Kenitra, Morocco;
    2. Department of Mathematics, Malayer University, P. O. Box 65719-95863, Malayer, Iran;
    3. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece
  • 收稿日期:2018-04-11 修回日期:2018-06-17 出版日期:2019-04-25 发布日期:2019-05-06
  • 通讯作者: Iz-iddine EL-FASSI E-mail:izidd-math@hotmail.fr;izelfassi.math@gmail.com
  • 作者简介:Hamid KHODAEI,hkhodaei.math@gmail.com;Themistocles M. RASSIAS,trassias@math.ntua.gr

APPROXIMATE SOLUTION OF A p-th ROOT FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN (2, β)-BANACH SPACES

Iz-iddine EL-FASSI1, Hamid KHODAEI2, Themistocles M. RASSIAS3   

  1. 1. Department of Mathematics, Faculty of Sciences, Ibn Tofaïl University, B. P. 133, Kenitra, Morocco;
    2. Department of Mathematics, Malayer University, P. O. Box 65719-95863, Malayer, Iran;
    3. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece
  • Received:2018-04-11 Revised:2018-06-17 Online:2019-04-25 Published:2019-05-06
  • Contact: Iz-iddine EL-FASSI E-mail:izidd-math@hotmail.fr;izelfassi.math@gmail.com

摘要: In this paper, using the Brzd?k’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

where p ∈ {1, …, 5}, a1, …, ak are fixed nonzero reals when p ∈ {1, 3, 5} and are fixed positive reals when p ∈ {2, 4}.

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

Abstract: In this paper, using the Brzd?k’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

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