Properties and integral inequalities of Hadamard- Simpson type for the generalized \((s,m)\)-preinvex functions

Volume 9, Issue 5, pp 3112--3126 http://dx.doi.org/10.22436/jnsa.009.05.102

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Authors

Ting-Song Du - College of Science, China Three Gorges University, 443002, Yichang, P. R. China. - Hubei Province Key Laboratory of System Science in Metallurgical Process, Wuhan University of Science and Technology, 430081, Wuhan, P. R. China. Jia-Gen Liao - College of Science, China Three Gorges University, 443002, Yichang, P. R. China. Yu-Jiao Li - College of Science, China Three Gorges University, 443002, Yichang, P. R. China.

Abstract

The authors introduce the concepts of m-invex set, generalized \((s,m)\)-preinvex function, and explicitly \((s,m)\)-preinvex function, provide some properties for the newly introduced functions, and establish new Hadamard-Simpson type integral inequalities for a function of which the power of the absolute of the first derivative is generalized \((s,m)\)-preinvex function. By taking different values of the parameters, Hadamardtype and Simpson-type integral inequalities can be deduced. Furthermore, inequalities obtained in special case present a refinement and improvement of previously known results.

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Keywords

• Integral inequalities of Hadamard-Simpson type
• Hölder's inequality
• \((s،m)\)-preinvex function.

MSC

•  26D15
•  26A51
•  26B12

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