[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b180385

THE k-GOLDEN MEAN OF TWO POSITIVE NUMBERS AND ITS APPLICATIONS

Choi, Jin Ho (Department of Mathematics Kyungpook National University)
Kim, Young Ho (Department of Mathematics Kyungpook National University)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.2, 2019 , pp. 521-533 More about this Journal

Abstract

In this paper, we define a mean of two positive numbers called the 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 k-golden ratio and give some properties of it as an generalization of the golden ratio. Furthermore, we define the matrix k-golden mean of two positive-definite matrices and give some properties of it. This is an improvement of Lim's results [2] for which the matrix golden mean.

Keywords

mean; arithmetic mean; geometric mean; harmonic mean; logarithmic mean; golden mean; golden ratio; golden spiral; positive definite matrix;

Citations & Related Records

Reference

1	M. Livio, The Golden Ratio, Broadway Books, New York, 2002.
2	P. Pesic, Music and the Making of Modern Science, London, MIT Press, 2014.
3	B. C. Carlson, The logarithmic mean, Amer. Math. Monthly 79 (1972), 615-618. DOI
4	Y. Lim, The matrix golden mean and its applications to Riccati matrix equations, SIAM J. Matrix Anal. Appl. 29 (2006/07), no. 1, 54-66. DOI