Inequalities on several quasi-arithmetic means

Shuoh-Jung Liu; Gou-Sheng Yang; Yi-Jhe Chen

doi:10.5556/j.tkjm.43.2012.841

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Published: Jun 20, 2012

DOI: https://doi.org/10.5556/j.tkjm.43.2012.841

Keywords:

convex functions concave functions means strictly increasing functions strictly decreasing functions.

Shuoh-Jung Liu

Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan, Republic of China.

Gou-Sheng Yang

Department ofMathematics Tamkang University, Tamsui 25137, Taiwan, Republic of China.

Yi-Jhe Chen

Department ofMathematics Tamkang University, Tamsui 25137, Taiwan, Republic of China.

Abstract

Inequalities on several quasi-arithmetic means are established by using convexity and concavity.

How to Cite

Liu, S.-J., Yang, G.-S., & Chen, Y.-J. (2012). Inequalities on several quasi-arithmetic means. Tamkang Journal of Mathematics, 43(2), 259–266. https://doi.org/10.5556/j.tkjm.43.2012.841

Issue

Vol. 43 No. 2 (2012)

Section

Papers

References

S. Abramovich, J. Pevcaric and S. Varovsance, Comparison Theorems between several quasi-arithmetic means, Math. Ineq. Appl., 7(2004), 1--6.

E. F. Beckenbach, R. Bellman, Inequalities, Spring-Verlag, Berlin-Newyork, 1961.

Y. H. Kim, Refinements and Extensions of an Inequality, J. Math. Anal. Appl., 245(2000), 628--632.

D. S. Mitrinovic, J. E. Pevcaric and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht/Boston/London, 1993.

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