Several improvements of Mitrinovic-Adamovic and Lazarevics inequalities with applications to the sharpening of Wilker-type inequalities

Volume 9, Issue 4, pp 1755--1765 http://dx.doi.org/10.22436/jnsa.009.04.31

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Authors

Shan-He Wu - Department of Mathematics, Longyan University, Longyan, Fujian, 364012, P. R. China. Huan-Peng Yue - Department of Mathematics, Longyan University, Longyan, Fujian, 364012, P. R. China. Yong-Ping Deng - Department of Mathematics, Longyan University, Longyan, Fujian, 364012, P. R. China. Yu-Ming Chu - School of Mathematics and Computation Science, Hunan City University, Yiyang, Hunan, 413000, P. R. China.

Abstract

In this paper, we give several improvements of Mitrinović-Adamović's inequality and Lazarević's inequality. Our results show some interesting relationships between Mitrinović-Adamović's inequality and Lazarević's inequality. At the end of the paper, the improved Lazarević's inequality is applied to the sharpening of Wilker-type inequalities for hyperbolic functions.

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Keywords

• Wilker-type inequalities
• hyperbolic functions
• Mitrinović-Adamović's inequality
• Lazarević's inequality
• improvement.

MSC

•  26D05
•  26D15
•  33B10

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