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, 。
Throughout the following of this section , e denotes a real banach space and p is a cone in e . in chapter , a new three - solution theorem is obtained . moreover , the famous amann ' s and leggett - williams " three - solution theorems in nonlinear functional analysis can be seen as its special cases , namely they are united . so they are improved . the main results can be stated as the following : let d be a nonempty bounded close convex subset in e , and nonnegative continuous functional on d . and is concave while is convex . suppose 0 < d and denote 首先我们约定,在下文中, e是实banach空间, p是e中的锥。在第一章中,我们利用锥理论与不动点指数理论统一了著名的amann三解定理与leggett - williams三解定理。主要结论是:设d是e中的非空有界闭凸集, ,是d上的非负连续泛函,且是凹泛函,是凸泛函。
Chapter 2 on the locally ( weakly ) uniform rotundity of musielak - orlicz sequence spaces : rotundity is important property in the geometry of banach space . in this paper , criterion that musielak - orlicz sequence spaces equipped with the orlicz norm and luxemburg norm is locally ( weakly ) uniformly rotund was discussed in detail . moreover , we get the sufficient and necessary condition of them 第二章musielak - orlicz序列空间的局部(弱)一致凸:凸性是banach空间几何理论的重要性质,本文详细讨论了赋orlicz范数和luxemburg范数的musielak - orlicz序列空间及它们的子空间的局部(弱)一致凸,并给出了它们的充分必要条件
The abstract cauchy problem and the fc - times integrated abstract cauchy problem play important roles in many practical problems . many equations and physics problems can be modeled as a abstract cauchy problem or a fc - times integrated abstract cauchy problem on a banach space , and the theories of semigroups provide us a very useful tool to investigate them Banach空间上抽象cauchy问题及-次积分抽象cauchy问题有着非常重要的实际作用,许多物理问题都可模式化为它们;在理论上,有些微分方程或是积分方程等也可以用它们表示
In this paper we discuss the convergence in the r - th mean and in probability for random weighted sums of random elements in a type p and b - convexity banach space , and give some necessary and sufficient conditions for the randomly weighted sums of the form vn anixni to converge , and also we give the convergence of weighted sums of martingale difference arrays of the form qnidni with values in a p - smoothable banach space . most of the previous papers discuss the randomly weighted sums of the form anixi 本文讨论了在p型和b凸banach空间上的随机加权和sumfromi = ntov _ na _ ( ni ) x _ ( ni )的平均收敛性及依概率收敛性,并从中给出了满足这些收敛性的充分与必要条件,以及在p阶光滑banach空间下鞅差阵列随机加权和sumfromi = ntov _ na _ ( ni ) d _ ( ni )的平均收敛性及依概率收敛性。
The existence of global solutions on interval [ 0 , a ] ( a > 0 ) for the first order initial value problem of discontinuous equations in banach space ( 1 ) is discussed . the fixed - point theorem of t - monotone increasing operators and the partial - ordered method are applied to these problems . an existence result is obtained . the results extend the relevant conclusions in reference [ 7 ] 利用t -单调增算子不动点定理和半序方法,得到了banach空间中含有间断项常微分方程初值问题( 1 )在[ 0 , a ] ( a 0 )上整体解的一个存在性结果,改进了文[ 7 ]中的相应结果。
The algorithm problem of solving the nonlinear operator equations f ( x ) = 0 in banach space has been one of the most interesting problems for many numerical scientists for a long time . at present time one of efficient algorithms to solve this problem is the iterative method . the king - werner method is a efficient one for solving the nonlinear equations 求解banach空间中非线性方程组算法问题,一直是数值工作者感兴趣的问题之一,迭代法是求解次类方程的一个重要算法同,解非线形方程组f ( x ) = 0的king - werner迭代法是一个计算效率较高的算法。