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


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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