Summary.
Let \(f:]0,\infty [ \to {\mathbb{R}}\) be a real valued function on the set of positive reals. Then the functional equations:
and
are equivalent to each other.
If \(f,g,h:]0,\infty [ \to {\mathbb{R}}\) are real valued functions on the set of positive reals then
is the Pexider generalization of
We find the general solution to this Pexider equation.
If \(f,g,h,k:]0,\infty [ \to {\mathbb{R}}\) are real valued functions on the set of positive reals then
is the Pexider generalization of
We find the twice differentiable solution to this Pexider equation.
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Manuscript received: May 11, 2004 and, in revised form, February 23, 2005.
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Heuvers, K.J., Kannappan, P. A third logarithmic functional equation and Pexider generalizations. Aequ. math. 70, 117–121 (2005). https://doi.org/10.1007/s00010-005-2792-8
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DOI: https://doi.org/10.1007/s00010-005-2792-8