Simpson-like type inequalities for relative semi-\((\alpha,m)\)-logarithmically convex functions
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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.
Share and Cite
ISRP Style
Chang Zhou, Cheng Peng, Tingsong Du, Simpson-like type inequalities for relative semi-\((\alpha,m)\)-logarithmically convex functions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 8, 4485--4498
AMA Style
Zhou Chang, Peng Cheng, Du Tingsong, Simpson-like type inequalities for relative semi-\((\alpha,m)\)-logarithmically convex functions. J. Nonlinear Sci. Appl. (2017); 10(8):4485--4498
Chicago/Turabian Style
Zhou, Chang, Peng, Cheng, Du, Tingsong. "Simpson-like type inequalities for relative semi-\((\alpha,m)\)-logarithmically convex functions." Journal of Nonlinear Sciences and Applications, 10, no. 8 (2017): 4485--4498
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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