共查询到19条相似文献,搜索用时 203 毫秒
1.
胡长松 《数学物理学报(A辑)》2004,24(2):216-222
该文研究了序列{x_n}的收敛性。其中x_0∈C, x_{n+1}=α_n T^n x_n+(1-α_n)x, n=0,1,2,…,这里0≤α_n≤1,T是Banach空间中非空闭凸子集C到自身的渐近非扩张映射。同时证明了:当z_n=(1-t_n/k_n)u+t_n/k_n T^n z_n且lim_{n→∞}{(k_n-1)/(1-t_n)}=0,lim‖z_n-Tz_n‖=0时,T有不动点当且仅当{z_n}有界。这时{z_n}强收敛于T的不动点。 相似文献
2.
该文研究了线性微分方程f″+e^{az}f′+Q(z)f=F(z)的复振荡问题,其中Q(z)、F(z )( 0)是整函数,且σ(Q)=1,σ(F)<+∞,Q(z)=h(z)e^{bz},h(z)是多项式,b≠-1是复常数,那么上述线性微分方程的所有解f(z)满足~λ(f)=λ(f)=σ(f)=∞,~λ_2(f)=λ_2(f)=σ_2(f)=1.至多除去两个例外复数a及一个可能的有穷级例外解f_0(z)。 相似文献
3.
K是Banach空间E的一个非空闭凸子集,T:K→K是一个广义Lipschitz伪压缩映射.对Lipschitz强伪压缩映射f:K→K和x_1∈K,序列{x_n}由下式定义:x_n+1=(1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.在{α_n}与{β_n}满足合适条件的情况下,每当{z∈K;μ_n‖x_n-z‖~2=inf_(y∈K)μ_n‖x_n-y‖~2}∩F(T)≠φ时,{x_n}强收敛到T的某个不动点x~*. 相似文献
4.
HU KE 《数学年刊A辑(中文版)》1981,2(1):21-24
Let \[\varphi (x) = \sum\limits_{k = 1}^\infty {{A_k}} {x^k},\Phi (x) = {e^{\varphi (x)}} = \sum\limits_{k = 1}^\infty {{D_k}} {x^k}\]
\[\begin{gathered}
\frac{1}{{{{(1 - x)}^\lambda }}} = \sum\limits_{k = 1}^\infty {{d_k}} (\lambda ){x^k} \hfill \ {\overline \Delta _n}(\lambda ) = {\lambda ^{2 - p}}\sum\limits_{k = 1}^\infty {{k^{p - 1}}} \mathop {|{A_k}|}\nolimits_{}^p - \sum\limits_{k = 1}^\infty {\frac{1}{k}} \hfill \\
\end{gathered} \]
Milin-Lebedey proved that
\[\sum\limits_{k = 0}^\infty {\frac{{|{D_k}{|^p}}}{{d_k^{p - 1}(\lambda )}}} \leqslant \exp \{ {\lambda ^{1 - p}}\sum\limits_{k = 1}^\infty {{k^{p - 1}}} |{A_k}{|^p}\} \]
where p>l and \[\lambda \]>0.
In this paper, we have proved the following theorems;
Theorem 1. Let \[p \geqslant 1,\lambda > 0\] and
\[F(x) = \sum\limits_{k = 0}^\infty {\frac{{|{D_k}{|^p}}}{{d_k^p(\lambda )}}} {x^p}\exp \{ - {\lambda ^{1 - p}}\sum\limits_{k = 1}^\infty {{k^{p - 1}}|{A_k}{|^p}{x^k}} \} (2)\]
then F(x) is a decreasing function of x on [0, 1].
This theorem is stronger than the result (1).
Theorem 2. Let \[p \geqslant 2,\lambda > 0\] and
\[{{\bar Q}_n}(\lambda ) = \frac{1}{{n + 1}}\sum\limits_{k = 0}^n {\frac{{|{D_k}{|^p}}}{{d_k^p(\lambda )}}\exp } \{ - \frac{1}{{n + 1}}\sum\limits_{v = 1}^n {\overline {{\Delta _p}} } (\lambda )\} \]
then \[{{\bar Q}_n}(\lambda )\] is a decreasing fimctLon of n(n=l, 2,...)In the case p=2 this is contained in the Miiin-Lebedev's result. 相似文献
5.
HU KE 《数学年刊B辑(英文版)》1981,2(1):21-24
Let \[\varphi (x) = \sum\limits_{k = 1}^\infty {{A_k}} {x^k},\Phi (x) = {e^{\varphi (x)}} = \sum\limits_{k = 1}^\infty {{D_k}} {x^k}\]
\[\begin{gathered}
\frac{1}{{{{(1 - x)}^\lambda }}} = \sum\limits_{k = 1}^\infty {{d_k}} (\lambda ){x^k} \hfill \ {\overline \Delta _n}(\lambda ) = {\lambda ^{2 - p}}\sum\limits_{k = 1}^\infty {{k^{p - 1}}} \mathop {|{A_k}|}\nolimits_{}^p - \sum\limits_{k = 1}^\infty {\frac{1}{k}} \hfill \\
\end{gathered} \]
Milin-Lebedey proved that
\[\sum\limits_{k = 0}^\infty {\frac{{|{D_k}{|^p}}}{{d_k^{p - 1}(\lambda )}}} \leqslant \exp \{ {\lambda ^{1 - p}}\sum\limits_{k = 1}^\infty {{k^{p - 1}}} |{A_k}{|^p}\} \]
where p>l and \[\lambda \]>0.
In this paper, we have proved the following theorems;
Theorem 1. Let \[p \geqslant 1,\lambda > 0\] and
\[F(x) = \sum\limits_{k = 0}^\infty {\frac{{|{D_k}{|^p}}}{{d_k^p(\lambda )}}} {x^p}\exp \{ - {\lambda ^{1 - p}}\sum\limits_{k = 1}^\infty {{k^{p - 1}}|{A_k}{|^p}{x^k}} \} (2)\]
then F(x) is a decreasing function of x on [0, 1].
This theorem is stronger than the result (1).
Theorem 2. Let \[p \geqslant 2,\lambda > 0\] and
\[{{\bar Q}_n}(\lambda ) = \frac{1}{{n + 1}}\sum\limits_{k = 0}^n {\frac{{|{D_k}{|^p}}}{{d_k^p(\lambda )}}\exp } \{ - \frac{1}{{n + 1}}\sum\limits_{v = 1}^n {\overline {{\Delta _p}} } (\lambda )\} \]
then \[{{\bar Q}_n}(\lambda )\] is a decreasing fimctLon of n(n=l, 2,...)In the case p=2 this is contained in the Miiin-Lebedev's result. 相似文献
6.
本文主要考虑以下两个问题: (1) 建立非齐次线性微分方程$$f''+A_2(z)f''+A_1(z)f''+A_0(z)f=A_3(z),$$ 系数增长性与解的零点的几何分布的相互关系, 其中 $A_0(z),\ldots, A_3(z)$为单位圆内的解析函数; (2) 找到一些使方程$$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_1(z)f''+A_0(z)f=0,$$ 所有解属于Zygmund-型空间的充分条件. 我们得到的结果推广了Heittokangas, Gr\"{o}hn, Korhoneon 和 R\"{a}tty\"{a}的部分结果. 相似文献
7.
本文主要研究一类复线性微分差分方程超越亚纯解的唯一性.特别地,假设$f(z)$为复线性微分差分方程: $W_{1}(z)f''(z+1)+W_{2}(z)f(z)=W_{3}(z)$的一个有穷级超越亚纯解,其中$W_{1}(z)$, $W_{2}(z)$, $W_{3}(z)$为增长级小于1的非零亚纯函数并且满足$W_{1}(z)+W_{2}(z)\not\equiv 0$.若$f(z)$与亚纯函数$g(z)$, $CM$分担0,1,$\infty$,则$f(z)\equiv g(z)$或$f(z)+g(z)\equiv f(z)g(z)$或$f^{2}(z)(g(z)-1)^2+g^{2}(z)(f(z)-1)^2=g(z)f(z)(g(z)f(z)-1)$或存在一个多项式$\varphi(z)=az+b_{0}$使得$f(z)=\frac{1-e^{\varphi(z)}}{e^{\varphi(z)}(e^{a_{0}-b_{0}}-1)}$与$g(z)=\frac{1-e^{\varphi(z)}}{1-e^{b_{0}-a_{0}}}$,其中$a(\neq 0)$, $a_{0}$ $b_{0}$均为常数且$a_{0}\neq b_{0}$. 相似文献
8.
李玉成 《数学物理学报(A辑)》2003,23(5):520-525
该文研究复Clifford分析中的超单演函数,即方程z_n Df(z)+(n-1)Qf′=0的解. 记f(z)=Pf(z)+Qf(z)e_n,f(z)∈C^2(Ω),f(z): Ω → C^{n+1},Ω C^{n+1},得出超单演函数的几个性质. 相似文献
9.
本文分别在复平面$\mathbb{C}$上和单位圆$\Delta$内考虑方程$$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_1(z)f''+A_0(z)f=0$$的解的增长性与其系数的增长性之间的关系.当$A_0(z)$或某个$A_j(z)(0相似文献
10.
应用锥上的不动点定理,建立了奇异非线性三点边值问题(u″(t)+a(t)f(u)=0,0<t<1,αu(0)-βu′(0)=0,u(1)-ku(η)=0)正解的一个存在性定理.这里η∈(0,1)是一个常数,a∈C( (0,1),[0,+∞)),f∈C([0,+∞),[0,+∞)) 相似文献
11.
The problem concerned in this paper is the set-valued equation 0 ∈T(z) where T is a maximal monotone operator. For given xk and βk > 0, some existing approximate proximal point algorithms take x~(k+1) = xk such thatwhere {ηk} is a non-negative summable sequence. Instead of xk+1 = xk , the new iterate of the proposing method is given bywhere Ω is the domain of T and PΩ(·) denotes the projection on Ω. The convergence is proved under a significantly relaxed restriction supk>0 ηk<1. 相似文献
12.
杜明笙 《应用数学学报(英文版)》1995,11(3):268-279
FINITEDIFFERENCESCHEMESOFTHENONLINEARPSEUDO-PARABOLICSYSTEMDUMINGSHENG(杜明笙)(InstituteofAppliedPhysicsandComputationalMathemat... 相似文献
13.
CHENG NAIDNG 《数学年刊B辑(英文版)》1980,1(2):214-222
In this paper,we have discussed constructive properties of a kind of uniformly
almost periodic functions, of which the sequence of its Fourier exponents has unique
limit point at infinity.
\[\begin{gathered}
f(x) \sim \sum\limits_{k = - \infty }^\infty {{A_k}} {e^{i{\Lambda _k}x}} \hfill \ {\Lambda _0} = \alpha ,0 < \alpha \leqslant {\Lambda _k} < {\Lambda _{k + 1}}(k = 0,1,2,...) \hfill \ \mathop {\lim }\limits_{k \to \infty } {\Lambda _k} = \infty ,{\Lambda _k} = - {\Lambda _k} \hfill \ |{\Lambda _k}| + |{\Lambda _{ - k}}| > 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (k \ne 0) \hfill \\
\end{gathered} \]
Analogons to the approximation theory of periodic functioiis, we get some theorems
similar to the Jackson theorem, Bernstein theorem and Zygmund theorem of periodio
functions. 相似文献
14.
《复变函数与椭圆型方程》2012,57(2):95-110
Let $ k \in {\shadN} $ , $ w(x) = (1+x^2)^{1/2} $ , $ V^{\prime} _k = w^{k+1} {\cal D}^{\prime} _{L^1} = \{{ \,f \in {\cal S}^{\prime}{:}\; w^{-k-1}f \in {\cal D}^{\prime} _{L^1}}\} $ . For $ f \in V^{\prime} _k $ , let $ C_{\eta ,k\,}f = C_0(\xi \,f) + z^k C_0(\eta \,f/t^k)$ where $ \xi \in {\cal D} $ , $ 0 \leq \xi (x) \leq 1 $ $ \xi (x) = 1 $ in a neighborhood of the origin, $ \eta = 1 - \xi $ , and $ C_0g(z) = \langle g, \fraca {1}{(2i \pi (\cdot - z))} \rangle $ for $ g \in V^{\,\prime} _0 $ , z = x + iy , y p 0 . Using a decomposition of C 0 in terms of Poisson operators, we prove that $ C_{\eta ,k,y} {:}\; f \,\mapsto\, C_{\eta ,k\,}f(\cdot + iy) $ , y p 0 , is a continuous mapping from $ V^{\,\prime} _k $ into $ w^{k+2} {\cal D}_{L^1}$ , where $ {\cal D}_{L^1} = \{ \varphi \in C^\infty {:}\; D^\alpha \varphi \in L^1\ \forall \alpha \in {\shadN} \} $ . Also, it is shown that for $ f \in V^{\,\prime} _k $ , $ C_{\eta ,k\,}f $ admits the following boundary values in the topology of $ V^{\,\prime} _{k+1} : C^+_{\eta ,k\,}f = \lim _{y \to 0+} C_{\eta ,k\,}f(\cdot + iy) = (1/2) (\,f + i S_{\eta ,k\,}f\,); C^-_{\eta ,k\,}f = \lim _{y \to 0-} C_{\eta ,k\,} f(\cdot + iy)= (1/2) (-f + i S_{\eta ,k\,}f ) $ , where $ S_{\eta ,k} $ is the Hilbert transform of index k introduced in a previous article by the first named author. Additional results are established for distributions in subspaces $ G^{\,\prime} _{\eta ,k} = \{ \,f \in V^{\,\prime} _k {:}S_{\eta ,k\,}f \in V^{\,\prime} _k \} $ , $ k \in {\shadN} $ . Algebraic properties are given too, for products of operators C + , C m , S , for suitable indices and topologies. 相似文献
15.
Let \[{\mathfrak{M}_k}\] denote the space of Lorentz witb. constant curvature:
\[1 + {K_{\eta pq}}{x^p}{x^q}\]
where K is a constant and \[\eta = ({\eta _{pq}})\]=diag [1,... 1,-1], We have considered the
wave equation with variable coefficients
\[\frac{\partial }{{\partial {x^j}}}(\sqrt {|\tilde g|} ){{\tilde g}^{jk}}\frac{{\partial u}}{{\partial {x^k}}}) = 0\]
in \[{\mathfrak{M}_k}\] where
\[|\tilde g| = |1 + {K_{\eta pq}}{x^p}{x^q}{|^{ - (n + 1)}},{{\tilde g}^{jk}} = (1 + {K_{\eta pq}}{x^p}{x^q})({\eta _{jk}} + K{x^j}{x^k})\]
and found the explicit solution of the Cauchy problem for equation (1) 相似文献
16.
D是C^n空间中具有逐块C(1)边界的有界域,该文建立了D上一个具有离散局部全纯核的(0,q)形式的Koppelman积分公式及其相应的方程解的积分表示和它的内闭一致估计式。 相似文献
17.
Bruno Pini 《Annali di Matematica Pura ed Applicata》1959,48(1):305-332
Sunto Si studia il problema della determinazione di una soluzione dell'equazione
ak(x)∂ku/∂xk=f(x, y) entro la semistriscia a≤x≤b, y≥0, che assuma assegnati valori per y=0 e per x=a, x1, x2, b (a<x1<x2<b). Analogamente si studia il problema della determinazione di una soluzione dell' equazione
ak(x)∂ku/∂xk+b(x)∂u/∂y=f(x,y), entro la medesima semistriscia, cha assuma assegnati valori per y=0 e per x=a, x1, x2, b e la cui ∂/∂y assuma assegnati valori per y=0.
A Giovanni Sansone nel suo 70mo compleanno. 相似文献
18.
O. N. Litvin 《Ukrainian Mathematical Journal》1992,44(11):1378-1384
A general algorithm is proposed for constructing interlineation operators
, x=(x1, x2) with the properties
相似文献
19.
In this paper, we establish two families of approximations for the gamma function: $$ \begin{array}{lll} {\varGamma}(x+1)&=\sqrt{2\pi x}{\left({\frac{x+a}{{\mathrm{e}}}}\right)}^x {\left({\frac{x+a}{x-a}}\right)}^{-\frac{x}{2}+\frac{1}{4}} {\left({\frac{x+b}{x-b}}\right)}^{\sum\limits_{k=0}^m\frac{{\beta}_k}{x^{2k}}+O{{\left(\frac{1}{x^{2m+2}}\right)}}},\\ {\varGamma}(x+1)&=\sqrt{2\pi x}\cdot(x+a)^{\frac{x}{2}+\frac{1}{4}}(x-a)^{\frac{x}{2}-\frac{1}{4}} {\left({\frac{x-1}{x+1}}\right)}^{\frac{x^2}{2}}\\ &\quad\times {\left({\frac{x-c}{x+c}}\right)}^{\sum\limits_{k=0}^m\frac{{\gamma}_k}{x^{2k}}+O{\left({\frac{1}{x^{2m+2}}}\right)}}, \end{array}$$ where the constants ${\beta }_k$ and ${\gamma }_k$ can be determined by recurrences, and $a$ , $b$ , $c$ are parameters. Numerical comparison shows that our results are more accurate than Stieltjes, Luschny and Nemes’ formulae, which, to our knowledge, are better than other approximations in the literature. 相似文献
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