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


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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