Some New Conclusions of Quasi-Semi-E-Convex Function

Generalized E-convex functions are the extension of convex function and have important applications in the study of optimization theory. Firstly,by researching the known properties of quasi-semi-E-convex function,some relative new properties of quasi-semi-E-convex functions were gained and proved. Secondly,the relationship between quasi-semi-E-convex function with quasi-E-convex function and semi-E-convex function were studied,some conclusions were obtained as well. Finally,a judging theorem of quasi- semi-E-convex function and a criterion of quasi-semi-E-convex function in the case of lower-semi-continuous were given.