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Computer assisted solution of an equality problem of mean values
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| Applied Mathematics and Computation |
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Given weighted quasi-arithmetic means M, N the problem is when the mean of the form u1 uðxÞ þ uðyÞ 1 2 ðuðMðx; yÞÞ þ uðNðx; yÞÞÞ is again quasi-arithmetic. It was answered in [5] by Daróczy and Páles under the assumption that M ¼ 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.
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Mean, Functional equation, Quasi-arithmetic mean, Conjugate mean
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