On the equality problem of two-variable Bajraktarević means under first-order differentiability assumptions
On the equality problem of two-variable Bajraktarević means under first-order differentiability assumptions
Abstract The equality problem of two-variable Bajraktarević means can be expressed as the functional equation $$\begin{aligned} \left( \frac{f}{g}\right) ^{-1}\bigg (\frac{f(x)+f(y)}{g(x)+g(y)}\bigg ) =\left( \frac{h}{k}\right) ^{-1}\bigg (\frac{h(x)+h(y)}{k(x)+k(y)}\bigg )\qquad (x,y\in I), \end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:msup> <mml:mfenced> <mml:mfrac> <mml:mi>f</mml:mi> <mml:mi>g</mml:mi> </mml:mfrac> </mml:mfenced> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> …