%0 Journal Article
%T Solving Invariant Problem of Cauchy Means Based on Wronskian Determinant
%A Yingjun Ni
%A Fen Wang
%J Advances in Pure Mathematics
%P 515-522
%@ 2160-0384
%D 2024
%I Scientific Research Publishing
%R 10.4236/apm.2024.147029
%X 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.
%K Cauchy Mean
%K Wronskian Determinant
%K Arithmetic Mean
%K Invariant Equation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=134702