The continuity and differentiability properties of quasi convex functions are discussed,and the specific properties of one real variable of the functions are also given.
讨论了拟凸函数的连续性和可微性。
The continuity and differentiability for composite function are the important content in advanced mathematics.
对高等数学中复合函数的连续性条件进行了弱化改进,得到了类似复合函数连续及在x0处极限存在的充分条件,对复合函数的可微性条件进行改进,得到了复合函数可微以及在x0处存在左右导数的充分条件。
Then the paper further gives the definition of the differentiability and its proof when n≥3,the function Z= f(x_1,x_2,……,x_n)is at M.
给出了Henle定理的简单证明 ,并指出该定理n≥ 3时不真 ,进而又给出了一个当n≥ 3时 ,函数z=f(x1,x2 ,… ,xn)在点M0 可微的定理及其证明。
Another Two Forms of Necessary and Sufficient Condition of Differentiable Complex Function;
复变函数可微性充要条件的另两种形式
The paper introduces a kind of differentiable fractal interpolation function,discusses its generating mechanismas well as the sufficient condition that generates its IFS.
文章介绍一类可微的分形插值函数,探讨了它的产生机理以及生成它的迭代函数系所满足的充要条件,在此基础上给出样条分形插值函数(SFIF)的定义,并讨论它所具有的部分收敛性质。
This paper studied a class of multiobjective programing problems involving differentiable n-set functions,and obtained sufficient optimality conditions for weak efficient solutions under generalized convexity conditions.
在较弱凸性条件下 ,研究了一类可微 n-集函数多目标规划问题的可行解是弱有效解的最优性充分条件。
in this paper, the author proves some equivalent forms of convex function definition, summarizes continuous and differential properties of convex function, obtains some useful results in mathematical programming, and verifies proposition 3.
本文证明了凸函数概念的一些等价形式；归纳了凸函数的连续性及可微性结论，得到了规划论中有用的极值命题；推证了简化多元凸函数讨论的命题３·１。
Furthermore,we obtain a sufficient and necessary condition about continuity of functional series and integral with parameter,and show the sufficient condition about differential.
将数学分析中一致收敛性的概念加以推广 ,分别对函数项级数和含参量积分引入次一致收敛的概念 ,证明了函数项级数、含参量非正常积分连续性的充要条件和可微性的充分条件 ,推广了数学分析中的相应结
This paper discusses the existence of partial derivative of x(or y) about a point (X_0, y_0) and analyzes conditions of continuance of X_0(or y_0) about function of y_1(or X_1)--f(x, y,) (or f(x, y) ), and puts forward a conditioned theorem, by which differential sufficient condition of a binary function can be demonstrated.
本文讨论在某一点(x0,y0)关于x(或y)的偏导数存在后对充分接近y0,(或x0)的y1(或x1)函数f(x,y1){或f(x1,y)},的y1是否存在x0(或y0)连续的条件作出分析,并给出有条件的定理1、并用其证明了一个二元函数的可微的充分条件。