Optimal generalized Heronian mean bounds for the logarithmic mean

Optimal Lower Generalized Logarithmic Mean Bound for the Seiffert Mean

Ying-Qing Song, Wei-Mao Qian, Yun-Liang Jiang, and Yu-Ming Chu 1 School of Mathematics and Computation Sciences, Hunan City University, Yiyang, Hunan 413000, China 2 School of Distance Education, Huzhou Broadcast and TV University, Huzhou, Zhejiang 313000, China 3 School of Information & Engineering, Huzhou Teachers College, Huzhou, Zhejiang 313000, China Correspondence should be addressed to Y...

Sharp bounds by the power mean for the generalized Heronian mean

* Correspondence: [email protected] Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China Full list of author information is available at the end of the article Abstract In this article, we answer the question: For p, ω Î R with ω >0 and p(ω 2) ≠ 0, what are the greatest value r1 = r1(p, ω) and the least value r2 = r2(p, ω) such that the double inequality Mr1 (a, b) ...

Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean

In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two posi...

Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means

Sharp Generalized Seiffert Mean Bounds for Toader Mean

and Applied Analysis 3 2. Lemmas In order to establish ourmain result, we need several formulas and lemmas, whichwe present in this section. The following formulas were presented in 10, Appendix E, pages 474-475 : Let r ∈ 0, 1 , then