### Abstract

Given three strict means M,N,K:ℝ_{+}^{2}→ ℝ^{+}, we say that the triple (M,N,K) satisfies the invariance equation ifKM(x,y),N(x,y)=K(x,y)(x,y∈ℝ^{+})holds. It is well known that K is uniquely determined by M and N, and it is called the Gauss composition M⊗N of M and N. Our aim is to solve the invariance equation when each of the means M,N,K is either a Gini or a Stolarsky mean with possibly different parameters. This implies that we have to consider six different invariance equations. With the help of the computer algebra system Maple V Release 9, which enables us to perform the tedious computations, we completely describe the general solutions of these six equations.

Original language | English |
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Pages (from-to) | 6297-6315 |

Number of pages | 19 |

Journal | Applied Mathematics and Computation |

Volume | 219 |

Issue number | 11 |

DOIs | |

Publication status | Published - Jan 31 2013 |

### Keywords

- Computer algebra
- Gauss composition
- Gini mean
- Invariance equation
- Stolarsky mean

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics