uniformly convex space 中文意思是什麼
uniformly convex space
解釋
一致凸空間-
Q - uniformly convex metric space and its application
一致凸度量空間及其應用 -
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， 。 -
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。 -
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。 -
The convergence theorms for asymptotically non - expanstive mapping in a uniformly convex banach space
空間漸近非擴張映像的收斂定理 -
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。 -
Asymptotically quasi - nonexpansive mapping with error members in a uniformly convex banach space
空間上漸近準非擴張映象 -
Weak convergence theorems for finite nonexpansive mappings in uniformly convex banach space
空間有限個非擴張映射的弱收斂 -
A character inequality for the uniformly convex banach space
空間的一個特徵不等式 -
Equivalent conditions of k - uniformly convex banach space
空間的等價條件
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