New Hermite-Hadamard inequalities for twice differentiable \(\phi\)-MT-preinvex functions

Volume 9, Issue 10, pp 5648--5660 http://dx.doi.org/10.22436/jnsa.009.10.11

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Authors

Sheng Zheng - College of Science, China Three Gorges University, 443002, Yichang, P. R. China. Ting-Song Du - College of Science, China Three Gorges University, 443002, Yichang, P. R. China. Sha-Sha Zhao - College of Science, China Three Gorges University, 443002, Yichang, P. R. China. Lian-Zi Chen - College of Science, China Three Gorges University, 443002, Yichang, P. R. China.

Abstract

New Hermite-Hadamard-type integral inequalities for \(\phi\)-MT-preinvex functions are obtained. Our results in special cases yield some of those results proved in recent articles concerning with the differentiable MTconvex functions. Some applications to special means and the trapezoidal formula are also considered, respectively.

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Keywords

• \(\phi\)-MT-preinvex functions
• Hermite-Hadamard's integral inequality
• Hölder's inequality.

MSC

•  26D15
•  26A51
•  26B12

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