拓扑半群 meaning in Chinese
topological semigroup
Examples
- Almost convex commutative topoloyical semigroups
几乎凸交换拓扑半群 - 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， 。