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open convex subset
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  开凸子集
     Differentiablity of continueous convex functions on a open convex subset D of Banach space X is discussed.
     给出若干定义在Banach空间开凸子集上的连续凸函数可微性的判据,它们可视为关于Banach空间的范数的可微性理论到一般连续凸函数上的推广.
短句来源
     The definition of norm ω * consistence continuity is introduced in this paper. It is shown that if the secondary derivative of a convex continuous function on banach space defined on an open convex subset of D is norm ω * consistence continuity on a dense subset of its domain,the function is gateaux differentiable on a dense G δ subset .
     通过引进了范—ω*一致连续的定义,指出了若Banach空间X中每个开凸子集D上定义的连续凸函数f(x)的次微分在D的一个稠集上范—ω*一致连续,则f(x)一定在D的一个稠Gδ集上Gateaux可微,从而X是ωAsplund空间
短句来源
     In this paper, it is proved that if E is separable and each continuous convex function on every open convex subset D of E is βdifferentiable at some point in D,then each weak compact convex subset of E is separable with respect to a metric which is weaker than or equal to the topology induced by β
     本文证明了如果可分Banach空间E的每个开凸子集D上的连续凸函数都在D中某一点β可微,则E*的每个有界弱. 闭凸子集关于其上弱于或等于由β导出的拓扑τβ的距离是可分的.
短句来源
     In this paper, it is shown that if a convex continuous function on Banach space defiend on an open convex subset of D is Gateaux differentiable on a dense subset of its domain, the function is Gateaux differentiable on a dense Gδ subset.
     给出并证明了:若Banach空间中开凸子集上定义的连续凸函数在其一个稠集上Gateaux可微,则它一定在其一个稠Gδ集上Gateaux可微。
短句来源
  “open convex subset”译为未确定词的双语例句
     In this paper, we prove following result: Let C be a nonempty open convex subset ofRn, f:C→R be upper semi-continuous function and there exists α∈(0, 1), such thatf[αx + (1-α)y]≤max{f(x), f(y)}, ∨x,y∈C,Then f is a quasiconvex function on C.
     在这篇文章里,证明了下述结果:设是非空开凸集,f是C上的上半连续函数且存在α∈(0,1),使得f(αx+(1-α)y≤max{f(x),f(y)},∨x》,y∈C则f为C上的拟凸函数.
短句来源
     Let X be a reflexive Banach space with both X and X * locally uniformly convex. D is a bounded, open, convex subset of X. T∶D→X * is a pseudo\|monotone operator;
     设 X是自反 Banach空间且 X和 X*均为局部一致凸空间 ,D是 X的开、有界、凸子集 ,T∶D→X*是伪单调算子 (pseudo-monotone) ,C∶D→ X*是紧算子或全连续算子 .
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  相似匹配句对
     open;
     评价的开放性问题;
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     Open fistulization for the treatment of rectal convex
     女性直肠前突开敞造瘘综合术78例对比观察
短句来源
     On the Existence of Minimal Convex Generated Set in the Open Set of E~n
     E~n中的开集不存在最小凸生成集
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     Open Nomenclature
     未定命名
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     On h Convex Function
     h凸函数
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  open convex subset
In this paper, we generalize a theorem of Benz by proving that if a mapping f, from an open convex subset of X into Y, has a contractive distance ρ and an extensive one Nρ (where N ≥ 2 is a fixed integer), then f is an isometry.
      
The author considers convex functionalsft defined on the open convex subset G of real B-space X and continuous at x0∈ G.
      


In this paper we prove the following:Let F: D R~n→R~n be Fre'chet differentiable on an open convex subset D with Assume that and let If,then{X_k} generated by Broyden method with projected update belong to N(X_o, r_o) and are convergente to the unique solution X of equations with n variables F(X)=O.

本文证明了下列事实: 设F∶D(?)R~n→R~n于开凸集D Frechet可微,F-导数满足今假定X_0∈D,B_0∈L(R~n),满足且设若则由投影修正Broyden算法所产生的序列{X_k}在N(X_0r_0)中且收敛于方程组F(X)=0的唯一解X。

Suppose that H is a Hilbert space,Ω is a bounded open convex subset in H,θ∈Q.Suppose that B:H→H is a pseudo-contractive mapping which satisfies Lipschitz condition,C:→>H is a strongly continuous mapping and A=B+C.In this paper we prove that if Axλx for x∈Ω,λ>1, then A has a fixed point in .

本文证明了拟压缩映射+强连续映射的若干不动点定理。

Differentiablity of continueous convex functions on a open convex subset D of Banach space X is discussed.

给出若干定义在Banach空间开凸子集上的连续凸函数可微性的判据,它们可视为关于Banach空间的范数的可微性理论到一般连续凸函数上的推广.

 
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