Xu, H.-Z., Chu, Y.-M. and Qian, W.-M. (2018) Sharp Bounds for the Sandor-Yang Means in Terms of Arithmetic and Contra-Harmonic Means. Journal of Inequalities and Applications, 2018, Article No.: 127.
https://doi.org/10.1186/s13660-018-1719-6

has been cited by the following article:

• TITLE: On Two Double Inequalities (Optimal Bounds and Sharps Bounds) for Centroidal Mean in Terms of Contraharmonic and Arithmetic Means

  AUTHORS: Mohammed El Mokhtar Ould El Mokhtar, Hamad Alharbi

  KEYWORDS: Centroidal Mean, Arithmetic Mean, Contraharmonic Mean

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.6, June 5, 2020

  ABSTRACT: This research work considers the following inequalities: λA(a,b) + (1-λ)C(a,b) ≤ C(a,b) ≤ μA(a,b) + (1-μ)C(a,b) and C[λa + (1-λ)b, λb + (1-λ)a] ≤ C(a,b) ≤ C[μa + (1-μ)b, μb + (1-μ)a] with. The researchers attempt to find an answer as to what are the best possible parameters λ, μ that (1.1) and (1.2) can be hold? The main tool is the optimization of some suitable functions that we seek to find out. By searching the best possible parameters such that (1.1) and (1.2) can be held. Firstly, we insert f(t) = λA(a,b) + (1-λ)C(a,b) - C(a,b) without the loss of generality. We assume that a>b and let to determine the condition for λ and μ to become f (t) ≤ 0. Secondly, we insert g(t) = μA(a,b) + (1-μ)C(a,b) - C(a,b) without the loss of generality. We assume that a>b and let to determine the condition for λ and μ to become g(t) ≥ 0.