Invariance of the Cauchy means with respect to Lagrange mean-type mappings of the same generators
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Without any regularity conditions, we determine all the Cauchy means C [f,g] that are invariant with respect to the mean-type mapping (L [f],L [g]) where L [f] denotes the Lagrangean mean generated by f. Applications in iteration theory and functional equation are given.
Key words and phrasesinvariant mean Cauchy mean Lagrangean mean differential equation functional equation
2000 Mathematics Subject Classification26E60 34A05 39B22
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- O. Sutô, Studies on some functional equations I, Tohŏku Math. J., 6 (1914), 1–15; II, ibid., 82–101. Google Scholar