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<p>This is an expository paper providing some simple observations on the best estimates in the Ulam stability of the Cauchy functional equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A(x+y)=A(x)+A(y)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. They have been motivated by a problem raised by Th.M.&#xa0;Rassias in connection with some early stability results obtained for the equation.</p>

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Notes on the best estimates in the Ulam stability of the Cauchy functional equation

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Janusz Brzdęk

摘要

This is an expository paper providing some simple observations on the best estimates in the Ulam stability of the Cauchy functional equation \(A(x+y)=A(x)+A(y)\) A ( x + y ) = A ( x ) + A ( y ) . They have been motivated by a problem raised by Th.M. Rassias in connection with some early stability results obtained for the equation.