On a functional equation related to two-variable Cauchy means
Abstract
In this paper, we are dealing with the solution of the functional equation (x+y2)(f(x)-f(y))=F(x)-F(y), concerning the unknown functions ,f and F defined on a same open subinterval of the reals. Improving the previous results related to this topic, we describe the solution triplets (,f,F) assuming only the continuity of . As an application, under natural conditions, we also solve the equality problem of two-variable Cauchy means and two-variable quasi-arithmetic means.
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