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<p>Following Khodaei [<CitationRef CitationID="CR11">11</CitationRef>], by using a new classical direct (Hyers) manner, we study some stability problems for a unified functional equation having monomials as solutions. Indeed, we obtain more exact approximations of the Ulam stability in comparison to the previous studies. In other words, we find Rassias stability results for the former functional equation in the setting of 2-Banach spaces. Eventually, by finding better error estimations, we improve some results obtained by Kang and Koh [A fixed point approach to the stability of sextic Lie <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivations, Filomat, 31 (2017), 4933-4944] for Lie <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivations of degree <i>n</i>.</p>

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On novel approximations of a functional equation having monomials

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Siriluk Donganont,
  • Abasalt Bodaghi

摘要

Following Khodaei [11], by using a new classical direct (Hyers) manner, we study some stability problems for a unified functional equation having monomials as solutions. Indeed, we obtain more exact approximations of the Ulam stability in comparison to the previous studies. In other words, we find Rassias stability results for the former functional equation in the setting of 2-Banach spaces. Eventually, by finding better error estimations, we improve some results obtained by Kang and Koh [A fixed point approach to the stability of sextic Lie \(*\) ∗ -derivations, Filomat, 31 (2017), 4933-4944] for Lie \(*\) ∗ -derivations of degree n.