Abstract. A functional equation involving pairs of means is considered. It is shown that there are only constant solutions if continuous differentiability is assumed, and there may be non-constant everywhere differentiable solutions. Various other situations are considered, where less smoothness is assumed on the unknown function.

DOI: 10.14232/actasm-015-805-1

AMS Subject Classification (1991): 39B22

Keyword(s): functional equation, means

Received June 4, 2014, and in revised form September 21, 2015. (Registered under 55/2015.)