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 The $k$-golden mean of two positive numbers and its applications Bull. Korean Math. Soc.Published online 2018 Sep 07 Jin Ho Choi, and Young Ho Kim Kyungpook National University Abstract : We define a mean of two positive numbers called the {\it $k$-golden mean} and study some properties of it. Especially, we show that the $2$-golden mean refines the harmonic and the geometric means. As an application, we define the {\it $k$-golden ratio} and give some properties of it as a generalization of the {\it golden ratio}. Furthermore, we define the matrix $k$-golden mean of two positive-definite matrices and give some properties of it. Keywords : mean, arithmetic mean, geometric mean, harmonic mean, logarithmic mean, golden mean, golden ratio, golden spiral, positive definite matrix MSC numbers : 15B48 Full-Text :

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