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1)  weak continuity of nonlinear functions
非线性泛函的弱连续性
2)  The Kernel of a Continuous Linear Functional
连续线性泛函的核
3)  Continuous fuzzy linear functional
连续的Fuzzy线性泛函
4)  continuous linear functional
连续线性泛函
1.
We give a sufficient & necessary condition for the Existence of non-trivial continuous linear functional on top-ological vector spaces, and show that there is no non-trivial continuous linear functional on any quasi-bounded topological vector space.
给出了拓扑线性空间上存在非零连续线性泛函的一个充要条件,并由此证明了在任意拟有界的拓扑线性空间上均不存在非零连续线性泛函。
2.
Under the necessary condition of an extremum of a continuous linear functional the least upper bound of Fourier coefficients of univalent harmonic mappings is obtained.
利用连续线性泛函取得极值的必要条件,得到关于单叶调和映射的傅立叶系数的上确界,推广了PeterDuren的研究方法。
3.
The necessary and sufficient condition for existing no non-zero continuous linear functional in spaces L ̄p(Ω,μ)(0<p<1)is there existing no atomic set in(Ω,μ).
空间L(Ω,μ)(0<p<1)上不存在非零连续线性泛函的充要条件是(Ω,μ)中不存在原子集合,2。
5)  continuous linear functionals
连续线性泛函
1.
The reflexity and the approximation property in Banach space X are studied by use of T semi inner product (x,y) T= lim t→0 +[(‖x+ty‖ 2-‖x‖ 2)/(2t)],x,y∈X and a class of continuous linear functionals T(X)={f x∈X *|〈f x,y〉=(x,y) T ;x,y∈X} is defined.
利用Tapia半内积(x,y)T=limt→0+[(x+ty2-x2)/(2t)],x,y∈X,研究了Banach空间X的自反和逼近性质,并在光滑的Banach空间X上利用由Tapia半内积定义的一类连续线性泛函T(X)={fx∈X*|〈fx,y〉=(x,y)T;x,y∈X}研究了Banach空间的严格凸、一致凸以及具有性质(H)的特征。
2.
This paper shows that, on a complete random normed module, there exists a nonzero continuous linear functional if and only if there is at least one atom in its base space; and there exist suffciently many nonzero continuous linear functionals if and only if its base is essentially generated by at most an countable family of atoms.
本文证明了在任意满支承的随机赋范模上存在一个非零连续线性泛函的充要条件是它的基底空间至少存在一个原子;存在足够多非零连续线性泛函的充要条件是它的基底空间本质上由至多可数个原子生成。
3.
This paper shows that on a complete random normed module,there exists a nonzero continuous linear functional if and only if there is at least an atom in its base space;and there exist sufficiently many nonzero continuous linear functionals if and only if its base is essentially generated by an at most countable family of atoms.
本文证明了在完备的随机赋范模上,存在一个非零连续线性泛函的充要条件是它的基底空间至少存在一个原子;存在足够多非零连续线性泛函的充要条件是它的基底空间本质上由至多可数个原子生成。
6)  bilinear continuous functional
双线性连续泛函
补充资料:非线性泛函


非线性泛函
non -linear fimctional

  非线性泛函「叨一血曰r加.尤伽司;肚瓜He如‘中,膝职OH幼] 定义在一个实(或复)向量空间X上的非线性算子(~,lj力ear ope正tor)的一个特殊情况,并且它的值是实(或复)数.非线性泛函的例子是变分学中的泛函 b ,(x)一丁;(,,x(。),x’(。))d亡,或者由条件 f(又y+(l一又)x)(又f(y)+(l一又)f(x)定义的凸泛函,其中x,y任X,O续又续1,以及,比如说,f(x)二”刘}—一个赋范空间中元素的范数. B .H.(为6QJIeB撰【补注1亦见非线性泛函分析(加n.枷。汀允飞加nal肛园娜is).鲁世杰译葛显良校
  
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