Some New Inequalities Between Important Means

Jamal Rooin; Mehdi Hassani

Some New Inequalities Between Important Means

Classical Analysis and ODEs 2007-10-22 v1

Authors: Jamal Rooin , Mehdi Hassani

Abstract

In this paper, mainly using the convexity of the function $\frac{a^x-b^x}{c^x-d^x}$ and convexity or concavity of the function $\ln\frac{a^x-b^x}{c^x-d^x}$ on the real line, where $a>b\geq c>d>0$ are fixed real numbers, we obtain some important relations between various important means of these numbers. Also, we apply the obtained results to Ky Fan type inequalities and get some new refinements.

Keywords

inequalities for means convex analysis inequalities

Cite

@article{arxiv.0710.3681,
  title  = {Some New Inequalities Between Important Means},
  author = {Jamal Rooin and Mehdi Hassani},
  journal= {arXiv preprint arXiv:0710.3681},
  year   = {2007}
}

Comments

Selected paper in 14th Seminar on Mathematical Analysis and its Applications, February 4-5, 2004, Iran University of Science and Technology, Tehran, Iran

Some New Inequalities Between Important Means

Abstract

Keywords

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