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<p>Using Brzdȩk’s fixed point technique, we investigate the Hyers-Ulam stability of the following functional equation: <Equation ID="Equa"> <EquationSource Format="TEX">\(\begin{aligned} a h\left( \frac{a xy}{x+y}\right) =h(x)+h(y) \end{aligned}\)</EquationSource> </Equation>for all <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x,y\in \mathbb {R}_{+}\)</EquationSource> </InlineEquation>, where <i>a</i> is a fixed positive real number.</p>

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Ulam stability of a generalized harmonic functional equation using Brzdȩk’s fixed point technique

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Yamin Sayyari,
  • Mehdi Dehghanian,
  • Yongqiao Wang,
  • Choonkil Park

摘要

Using Brzdȩk’s fixed point technique, we investigate the Hyers-Ulam stability of the following functional equation: \(\begin{aligned} a h\left( \frac{a xy}{x+y}\right) =h(x)+h(y) \end{aligned}\) for all \(x,y\in \mathbb {R}_{+}\) , where a is a fixed positive real number.