banach theorem 中文意思是什麼
-
Eigenvalue theorem on near - algebra and banach algebra
代數上的一個特徵值定理 -
Hahn - banach functional extension theorem and it ' s annlication
泛函延拓定理及其應用 -
In latter part of chapter three, some exciting properties of the revised lagrangian function discussed first, which leads to form a dual algorithm of cora or cot. convergence theorem proved by banach perturbation theorem, bertsekas implicit function theorem ii and by analyzing hesse matrix of revised largrangian function
另一類是構造相應的lagrange函數及其一種對偶演算法的迭代格式，討論了修正lagrange函數的性質，並藉助banach擾動定理及bertsekas第h隱函數定理，及對修正lagrange函數hesse陣分析，證明了該演算法的收斂性 -
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
近年來， bruck [ 5 ] ， reich [ 6 ] ， oka [ 7 ]等在具frechet可微范數的一致凸banach空間中給出了非擴張及漸近非擴張映射及半群的遍歷收斂定理。 li和ma [ 13 ]在具frechet可微范數的自反banach空間中給出了一般交換漸近非擴張型拓撲半群的遍歷收斂定理，這是一個重大突破。本文第二章用一種新的證明方法在自反banach空間中，研究了揚州大學碩士學位論文2一般半群上的（ r ）類漸近非擴張型半群的弱遍歷收斂定理，即:定理3 . 1設x是具性質（ f ）的實自反banach空間， c是x的非空有界閉凸子集， g為含單位元的一般半群， s =仕工， 。 -
Sufficient conditions are obtained for the existence of bounded positive solutions of the n - order delay differential equations with nonlinear neutral term, on the basis of lebesgue ' s monotone convergence theorem and banach contraction theorem
摘要利用控制收斂定理和壓縮映射原理研究了一類具非線性中立項時滯微分方程有界正解的存在性，獲得了其存在有界正解的充分條件。 -
By using bruck ' s lemma [ 10 ], passty [ 31 ] extended the results of [ 1, 16 ] to uniformly convex banach space with a frechet differentiable norm. however, there existed more or less limitations in their methods adopted. by using new techniques, chapter2 of this paper discussed the weak convergence theorem for right reversible semigroup of asymptotically nonexpansive type semigroup and the corresponding theorem for its almost - orbit in the reflexive banach space with a frechet differentiable norm or opial property
Feattieranddotson 16 ]和bose [ l ]通過使用opial引理17 }在具弱連續對偶映照的一致凸b ~ h空間中證明了漸近非擴張映照的弱收斂定理， passty 31通過使用bruck引理10 ]把1 ， 16 ]的結果推廣到具freehet可微范數的一致凸banach空間，然而，他們的證明存在著種種局限性。 -
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
首先我們約定，在下文中， e是實banach空間， p是e中的錐。在第一章中，我們利用錐理論與不動點指數理論統一了著名的amann三解定理與leggett - williams三解定理。主要結論是：設d是e中的非空有界閉凸集， ，是d上的非負連續泛函，且是凹泛函，是凸泛函。 -
The convergence theorem of the triple ishikawa iterative with errors for nonexpansive mappings in a uniformly convex banach spaces
型的三重迭代序列的收斂性 -
A theorem of iterative approximation of zero point for maximal monotone operator in banach space
空間中極大單調運算元零點的迭代逼近定理 -
Secondly, the above priori estimates and the banach - saks theorem provide the existence of h1 weak solution for the auxiliary problems without small parameter e
因此，不難得到輔助問題分別在每個區域上的全局h ~ 1估計。 -
Reich [ 2 ] proved the ergodic theorems to nonexpansive semigroups in hilbert spaces. takahashi and zhang [ 3 ], tan and xu [ 4 ] extended baillon ' s theorem to asymptotically nonexpansive and asymptotically nonexpansive type semigroups in hilbert spaces. recently, reich [ 6 ], bruck [ 5 ], oka [ 7 ] gave the ergodic convergence theorems for nonexpansive, asymptotically nonexpansive mappings and semigroups in uniformly convex banach spaces with frechet differentiable norm. li and ma [ 13 ] obtained the ergodic convergence theorems for general commutative asymptotically nonexpansive type topological semigroups in reflexive banach space, which is a great breakthrough
Baillon [ 1 ]首先在hilbert空間的非空凸閉子集上給出了非擴張映照的弱遍歷收斂定理。 baillon的定理引起了很多數學家的興趣， reich [ 2 ]在hilbert空間中證明了非擴張半群的遍歷收斂定理。 takahashi和zhang [ 3 ] ， tan和xu [ 4 ]分別將baillon的定理推廣到漸近非擴張半群及漸近非擴張型半群。 -
Main results : theorem 1 let e be a real banach space, p be a normal cone in e. conditions ( a1 ) - ( a3 ) be satisfied, let k0 < c2, and l = max { 1, maxj g ( t, s ) }, inequality 4l # [ c3 + m + 47 # k0 ( c4 + 2n ) ] < 1 holds. then there exist monotone sequences { vn ( t ) }, ( wn ( t ) }, such that uniformly on i and p ( t ], r ( t ) are minimal and maximal solutions between vq and w0 forpbvp ( 1. 1 )
（ a2 ）存在常數m o ， n 0 ，滿足這里（ a3 ）對和等度連續的有界單調序列都有其中本文的主要定理：定理設為實空間， p是中正規錐，條件滿足，設設滿足則存在單調序列在上一致成立，且分別為上的最小解和最大解 -
To the first equation, the banach contraction mapping theorem is used to show the local existence of the solutions, we use potintial well method to prove the global existence and the decay rate of the solutions, to the blow - up of the solution we use the energy method
本文主要採用bananch壓縮映射原理來獲得解的局部存在性；採用勢井方法來獲得解的整體存在性和衰減估計；對解的爆破結論的證明主要採用能量方法；對解的能量衰減估計主要採用能量擾動方法。 -
In this paper, we have proved that an anti - bounded c _ ( 0 ) - group in infinite - dimensional reflexive banach spaces is not exponentially stable under generating compact perturbation, and that a c _ ( 0 ) - isometric semigroup in infinite - dimensional hilbert spaces has the same property. so, we have extended and improved russell theorem
在本文中，我們分別證明了無限維自反banach空間中的反有界c _ 0 -群和無限維hilbert空間中的c _ 0 -等距半群在生成的緊擾動下一定不具指數穩定性，從而推廣和改進了russell定理。 -
In 1982, a weak convergence theorem for nonexpensive semigroups in uniformly convex banach space was first established by miyadera and kobaysi and it was generalized to that for commutative semigroup of asymptotically nonexpansive mappings by oka [ 15 ]. feathers and dotson [ 16 ] and bose [ 1 ] gave the weak convergence theorem of asymptotically nonexpansive mappings in a uniformly convex banach space with weak continuous duality mapping by using opial ' s lemma [ 17 ]
也正是由miyadera和kobayasi於1982年首次在一致凸banach空中給出了非擴張半群的弱收斂定理，隨后，由okaf15 ]把此弱收斂定理推廣到交換半群的漸近非擴張映照。 -
Hahn - banach theorem
罕-巴拿赫定理 -
Banach fixed - point theorem and its randomization
不動點定理及其隨機化 -
In the third chapter, we derive a new family of deformed halley methods without the evaluation of the second frechet - derivative to approximate the roots of nondifferentiable equations in banach space. we also provided a existence - uniqueness theorem and a new system of recurrence relations
在第三章中，構造了一族避免二階fre chet導數的修正halley迭代，用其去逼近banach空間中非線性運算元方程的解，同時給出了存在唯一性定理和一種新型的遞歸關系。 -
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 -單調增運算元不動點定理和半序方法，得到了banach空間中含有間斷項常微分方程初值問題（ 1 ）在[ 0 ， a ] （ a 0 ）上整體解的一個存在性結果，改進了文[ 7 ]中的相應結果。 -
3. as for the existence of positive solutions, the cone theory and the fixed point index of condensing mapping are employed, and the results of the existence of positive solutions are obtained in the case of superlinear and sublinear. the conclusions extend and improve the existence theorem which lou ben - dong extablished in 1996 about the question of sturm - liouville of banach spaces
三、對于正解存在性問題，我們應用凝聚映射的不動點指數理論，分別在超線性與次線性情形下進行討論，獲得了一些正解存在的結果，主要結果推廣和改進了1996年louben - dong對banach空間sturm - liouville問題所建立的存在性定理。
分享友人