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Computer assisted solution of an equality problem of mean values

Judita Dascal
Justyna Jarczyk
Journal / Anthology

Applied Mathematics and Computation
Year: 2012
Volume: 219
Page range: 475481

Given weighted quasi-arithmetic means M, N the problem is when the mean of the form u1 ux uy  1 2 uMx; y uNx; y   is again quasi-arithmetic. It was answered in [5] by Darczy and Ples under the assumption that M N is arithmetic. We investigate the complementary situation where at least one of the weighted arithmetic means M, N is not arithmetic and solve the problem locally, assuming that the generators of means are four times continuously differentiable. For the computation we use the software package Mathematica 4.0.

*Applied Mathematics

Mean, Functional equation, Quasi-arithmetic mean, Conjugate mean