凸子集 meaning in Chinese
convex subset
Examples
- In certain case it might be necessary to further decompose a spiral into convex subsets .
在某些情况下，把一个螺旋形进一步分解成凸子集是必要的。 - The maximal value point s problem of a convex function on a closed convex subset in locally convex space is considered by using the level set of function , - subdifferential and - normal cone . it gives several equivalent characters on the optimal solutions of the problem
利用函数的水平集， -次微分和-法向锥等工具研究局部凸空间的凸函数在闭凸子集上的最大值点问题，给出了最优解的几个等价刻划 - Chapter 2 of this paper , by using a new method of proof , we obtain the weak ergodic convergence theorem for general semigroups of asymptotically nonexpansive type semigroups in reflexive banach space . by theorem 2 . 1 of chapter 1 we get the weak ergodic convergence theorem of almost orbit for general semigroups of asymptotically nonexpansive type semigroups in reflexive banach space . by this method of proof , we give the weak ergodic convergence theorems for right reversible semigroups . by theorem 2 . 1 of chapter l , we generalize the result to almost orbit case . so we can remove a key supposition that almost orbit is almost asymptotically isometric . it includes all commutative semigroups cases . baillon [ 8 ] , hirano and takahashi [ 9 ] gave nonlinear retraction theorems for nonexpansive semigroups . recently mizoguchi and takahashi [ 10 ] proved a nonlinear ergodic retraction theorem for lipschitzian semigroups . hirano and kido and takahashi [ 11 ] , hirano [ 12 ] gave nonlinear retraction theorems for nonexpansive mappings in uniformly convex banach spaces with frechet differentiable norm . . in 1997 , li and ma [ 16 ] proved the ergodic retraction theorem for general semitopological semigroups in hilbert space without the conditions that the domain is closed and convex , which greatly extended the fields of applications of ergodic theory . chapter 2 of this paper , we obtain the ergodic retraction theorem for general semigroups and almost orbits of asymptotically nonexpansive type semigroups in reflexive banach spaces . and we give the ergodic retraction theorem for almost orbits of right reversible semitopological semigroups
近年来， bruck [ 5 ] ， reich [ 6 ] ， oka [ 7 ]等在具frechet可微范数的一致凸banach空间中给出了非扩张及渐近非扩张映射及半群的遍历收敛定理。 li和ma [ 13 ]在具frechet可微范数的自反banach空间中给出了一般交换渐近非扩张型拓扑半群的遍历收敛定理，这是一个重大突破。本文第二章用一种新的证明方法在自反banach空间中，研究了扬州大学硕士学位论文2一般半群上的( r )类渐近非扩张型半群的弱遍历收敛定理，即:定理3 . 1设x是具性质( f )的实自反banach空间， c是x的非空有界闭凸子集， g为含单位元的一般半群， s =仕工， 。