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.