| Convex set is the elementary concept of Convex Analysis.It is important to the research of optimal control problem.The article discusses that the concept of strongly convex set is inaccurate in related literature and introduces generalized strongly convex and standard strongly convex function. Some relations and classified problems are presented among them.Convex functions are significant and have extensive application in the field of optimal control and fixed point and approximation theory etc.Some elementary properties are further discussed about generalized strongly convex set and function.Then the article puts forward classified criterions and defined methods of strongly convex function.Some valuable results of standard classification are proved of strongly convex function.For example ,descriptive theorm of minimal standard strongly convex function.Discussed spheres of usual strongly convex and function are promoted and have partly theoretical reference values for optimal control. |
