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<p>The main purpose of this article is to investigate the Hyers-Ulam stability of the following <i>n</i>-dimensional quadratic functional equation of the form <Equation ID="Equ27"> <EquationSource Format="TEX">\(\begin{aligned} \mathfrak {g}\ \bigg (\sum _{i=1}^{k} \nu _{i} \bigg ) \ \ = \sum _{1\le i&lt;j\le k} \mathfrak {g}\big (\nu _{i}+\nu _{j}\big )-(s-6) \sum _{i=1}^{k} \mathfrak {g}(\nu _{i}) - \sum _{i=1}^{k} \mathfrak {g} \big ( -2 \nu _{i}\big ) \end{aligned}\)</EquationSource> </Equation>in non-Archimedean quasi-<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\beta \)</EquationSource> </InlineEquation>-normed spaces by using the direct method and fixed point method.</p>

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Ulam stability of quadratic n-dimensional functional equations in non-Archimedean quasi-\(\beta \)-normed spaces

  • 期刊论文

  • 发表日期：

    2026年3月27日

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  • Paramasivam Elumalai,
  • Sampath Sangeetha,
  • Siriluk Donganont,
  • Choonkil Park,
  • Arumugam Ponmana Selvan

摘要

The main purpose of this article is to investigate the Hyers-Ulam stability of the following n-dimensional quadratic functional equation of the form \(\begin{aligned} \mathfrak {g}\ \bigg (\sum _{i=1}^{k} \nu _{i} \bigg ) \ \ = \sum _{1\le i<j\le k} \mathfrak {g}\big (\nu _{i}+\nu _{j}\big )-(s-6) \sum _{i=1}^{k} \mathfrak {g}(\nu _{i}) - \sum _{i=1}^{k} \mathfrak {g} \big ( -2 \nu _{i}\big ) \end{aligned}\) in non-Archimedean quasi- \(\beta \) -normed spaces by using the direct method and fixed point method.