Volume 49, Issue 1
Some Improvements on Hermite-Hadamard's Inequalities for $s$-Convex Functions

J. Math. Study, 49 (2016), pp. 82-92.

Published online: 2016-03

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• Abstract

Using an integral identity for a once differentiable mapping, this paper establishes Hadamard's integral inequalities for $s$-convex and $s$-concave mappings. In particular, our results improve and extend some known ones in the literature. Finally, these inequalities are applied to special means.

• Keywords

Convex function, $s$-convex function, Hadamard's inequality.

26D15, 26A51, 26E60, 41A55

yujiaolictgu@163.com (Yujiao Li)

tingsongdu@ctgu.edu.cn (Tingsong Du)

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@Article{JMS-49-82, author = {Yujiao and Li and yujiaolictgu@163.com and 13314 and Department of Mathematics, Science College, China Three Gorges University, Yichang 443002, Hubei, P.R. China and Yujiao Li and Tingsong and Du and tingsongdu@ctgu.edu.cn and 13315 and Department of Mathematics, Science College, China Three Gorges University, Yichang 443002, Hubei, P.R. China and Tingsong Du}, title = {Some Improvements on Hermite-Hadamard's Inequalities for $s$-Convex Functions}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {1}, pages = {82--92}, abstract = {

Using an integral identity for a once differentiable mapping, this paper establishes Hadamard's integral inequalities for $s$-convex and $s$-concave mappings. In particular, our results improve and extend some known ones in the literature. Finally, these inequalities are applied to special means.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n1.16.10}, url = {http://global-sci.org/intro/article_detail/jms/992.html} }
TY - JOUR T1 - Some Improvements on Hermite-Hadamard's Inequalities for $s$-Convex Functions AU - Li , Yujiao AU - Du , Tingsong JO - Journal of Mathematical Study VL - 1 SP - 82 EP - 92 PY - 2016 DA - 2016/03 SN - 49 DO - http://doi.org/10.4208/jms.v49n1.16.10 UR - https://global-sci.org/intro/article_detail/jms/992.html KW - Convex function, $s$-convex function, Hadamard's inequality. AB -

Using an integral identity for a once differentiable mapping, this paper establishes Hadamard's integral inequalities for $s$-convex and $s$-concave mappings. In particular, our results improve and extend some known ones in the literature. Finally, these inequalities are applied to special means.

Yujiao Li & Tingsong Du. (2019). Some Improvements on Hermite-Hadamard's Inequalities for $s$-Convex Functions. Journal of Mathematical Study. 49 (1). 82-92. doi:10.4208/jms.v49n1.16.10
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