Optimal Two Parameter Bounds for the Seiffert Mean

Optimal Bounds for Seiffert Mean in terms of One-Parameter Means

Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean

and Applied Analysis 3 2. Proof of Theorem 1.1 Proof of Theorem 1.1. Let λ 1 √ 4/π − 1 /2 and μ 3 √3 /6. We first proof that the inequalities T a, b > C λa 1 − λ b, λb 1 − λ a , 2.1 T a, b < C ( μa ( 1 − μb, μb 1 − μa 2.2 hold for all a, b > 0 with a/ b. From 1.1 and 1.2 we clearly see that both T a, b and C a, b are symmetric and homogenous of degree 1. Without loss of generality, we assume th...

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

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...

Two sharp double inequalities for Seiffert mean

* Correspondence: [email protected] Department of Mathematics, Huzhou Teachers College, Huzhou 313000, People’s Republic of China Full list of author information is available at the end of the article Abstract In this paper, we establish two new inequalities between the root-square, arithmetic, and Seiffert means. The achieved results are inspired by the paper of Seiffert (Die Wurzel, ...