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Głazowska, D. (2011) Some Cauchy Mean-Type Mappings for Which the Geometric Mean Is Invariant. Journal of Mathematical Analysis and Applications, 375, 418-430.
https://doi.org/10.1016/j.jmaa.2010.09.036

has been cited by the following article:

• TITLE: Solving Invariant Problem of Cauchy Means Based on Wronskian Determinant

  AUTHORS: Yingjun Ni, Fen Wang

  KEYWORDS: Cauchy Mean, Wronskian Determinant, Arithmetic Mean, Invariant Equation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.14 No.7, July 23, 2024

  ABSTRACT: This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtained by using the method of Wronskian determinant in the process of solving. Then the invariant equation is solved by using the obtained partial derivatives. Finally, the solutions of invariant equations when the denominator functions satisfy the same simple harmonic oscillator equation or the denominator functions are power functions that have been obtained.