Results on comparison and sub/super-stabilizability of some new means
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909209798377472 |
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| author | Mihoković, Lenka Raïssouli, Mustapha |
| author_facet | Mihoković, Lenka Raïssouli, Mustapha |
| contents | We present analysis of some new means recently introduced by M. Raïssouli and A. Rezgui. We establish comparison relations and results on $(K,N)$-sub/super-stabilizability where $K$ and $N$ belong to the class of power means, denoted by $B_p$, and $M$ is one of the classical or recently studied new means. Assuming that means $K$, $M$ and $N$ have asymptotic expansions, we present the complete asymptotic expansion of the resultant mean-map. As an application of the obtained asymptotic expansions and the asymptotic inequality between $M$ and $\mathcal{R}(B_p,M,B_q)$, we show how to find the optimal parameters $p$ and $q$ for which $M$ is $(B_p,B_q)$-sub/super-stabilizable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Results on comparison and sub/super-stabilizability of some new means Mihoković, Lenka Raïssouli, Mustapha Classical Analysis and ODEs 26E60, 41A60, 39B62 We present analysis of some new means recently introduced by M. Raïssouli and A. Rezgui. We establish comparison relations and results on $(K,N)$-sub/super-stabilizability where $K$ and $N$ belong to the class of power means, denoted by $B_p$, and $M$ is one of the classical or recently studied new means. Assuming that means $K$, $M$ and $N$ have asymptotic expansions, we present the complete asymptotic expansion of the resultant mean-map. As an application of the obtained asymptotic expansions and the asymptotic inequality between $M$ and $\mathcal{R}(B_p,M,B_q)$, we show how to find the optimal parameters $p$ and $q$ for which $M$ is $(B_p,B_q)$-sub/super-stabilizable. |
| title | Results on comparison and sub/super-stabilizability of some new means |
| topic | Classical Analysis and ODEs 26E60, 41A60, 39B62 |
| url | https://arxiv.org/abs/2405.13618 |