Sharp bounds for the lemniscatic mean by the weighted Holder mean

被引：4
作者：
Zhao, Tie-hong [1 ]
Wang, Miao-kun [2 ]
机构：
[1] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China
[2] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2023年 / 117卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Lemniscate functions; Lemniscatic mean; Weighted Holder mean; Gaussian hypergeometric function; TRANSFORMATION INEQUALITIES; MONOTONICITY; WILKER;
D O I：
10.1007/s13398-023-01429-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper deals with Gauss arc lemniscate functions and the lemniscatic mean LM(x, y). It has been proved in [Neuman (Math Pannon 18(1): 77-94, 2007), Lemma 4.1] that the double inequality x(3/5) y(2/5) < LM(x, y) < 3x + 2y/5 holds for x, y > 0 with x not equal y. This can be extended to approximate the lemniscatic mean by the weighted Holder mean. As applications, several new bounds for the arc lemniscate functions are also derived, which improve some previously known results.
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页数：19
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