The Criterions Of Convex Function And Generalized Convex Functions Under The Weaker Conditions

Convex function and generalized convex functions are important components of convex analysis;they have important applications in the optimization theory and other disciplines.In this paper,the discriminant criterions of convex function and five types generalized convex functions are studied under the weaker conditions.In the first chapter,we introduce the research status of convex function and generalized convex functions.In the second chapter,we introduce some concepts,relations and properties of convex function and generalized convex functions.In the third and fourth chapters,the results of three aspects are obtained through the study of the discriminant criterions of convex function and five types generalized convex functions under the weak conditions.Firstly,under the weaker conditions,we prove that the related sets of convex function,strict convex function,quasi-convex function and strict quasiconvex function are dense in [0,1].Secondly,some new criterions for convex function,strict convex function,semi-strict convex function,quasi-convex function,strict quasi-convex function and semi-strict quasi-convex function are obtained by using the density of related sets.Thirdly,through some examples,the results of this thesis under the weaker conditions are compared with some known results under the stronger conditions.