Simpson-like type inequalities for relative semi-\((\alpha,m)\)-logarithmically convex functions

Volume 10, Issue 8, pp 4485--4498 http://dx.doi.org/10.22436/jnsa.010.08.40

Publication Date: August 29, 2017 Submission Date: June 08, 2017

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Authors

Chang Zhou - Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, Hubei, P. R. China. Cheng Peng - Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, Hubei, P. R. China. Tingsong Du - Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, Hubei, P. R. China.

Abstract

In this paper, we derive a new integral identity concerning differentiable mappings defined on relative convex set. By using the obtained identity as an auxiliary result, we prove some new Simpson-like type inequalities for mappings whose absolute values of the first derivatives are relative semi-\((\alpha,m)\)-logarithmically convex. Several special cases are also discussed.

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Keywords

• Relative semi-((\alpha
• m)\)-logarithmically convex
• Simpson’s inequality
• Hölder’s inequality
• Young inequality.

MSC

•  26A33
•  26A51
•  26D07
•  26D20
•  41A55

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