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2019-10-05 15:37发布

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```tex \documentclass[12pt,a4]{article} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{amsfonts} \usepackage{amsthm} \usepackage{amsmath,mathrsfs} \usepackage{amssymb} \usepackage{graphicx} \usepackage{subfig} \usepackage{cite} \setcounter{MaxMatrixCols}{10} %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Version=5.00.0.2606} %TCIDATA{} %TCIDATA{BibliographyScheme=Manual} %TCIDATA{LastRevised=Monday, April 29, 2013 16:28:32} %TCIDATA{} %TCIDATA{Language=American English} \topmargin -0.5cm \oddsidemargin -0.5cm \evensidemargin -0.5cm \textwidth=17 true cm \textheight=23.2 true cm %\input{tcilatex} \begin{document} \title{ Parallel *** in Hilbert space } \author{*** $^{1,}$\thanks{Corresponding author.}, ??? $^2$ \\ \\ \footnotesize{$^1$ Department of Mathematics, *** University}\\ \footnotesize{ ***, China}\\ \footnotesize{ $^2$ Department of Engineering, *** University}\\ \footnotesize{ ***, China}\\ \\ \\ \\ \footnotesize{ E-mails: ???@163l.com} } \date{} \maketitle {\footnotesize \noindent \textbf{Abstract.} \vskip 0.2cm } {\footnotesize \noindent \textbf{Keywords}: .\vskip 1mm } {\footnotesize \noindent \textbf{2010 AMS Subject Classification}: } \vskip 4mm \section*{1. Introduction} \vskip 0.5cm \section*{2. Preliminaries}\vskip 2mm \section*{3. Main results} \vskip0.3cm \newpage where $\{\alpha_n\}\subset(0,1)$, $\rho\in(0,\min\{\frac{1}{2c_1},\frac{1}{2c_2}\}$. If $\lim_{n\to\infty}\alpha_n=0$, then $\{x_n\}$ generated by $(3.20)$ converges strongly to element $\hat{x}=P_\Omega x_1.$ \vskip0.2cm \noindent {\bf Remark 3.2} If $U_i\equiv U$ for each $i=1,\ldots, N$ and $V_j\equiv V$ for each $j=1,\ldots, M$ in Theorems 3.1 and 3.2, we obtain the corresponding results announced in \cite[Theorem 1,Theorem 2]{HieuMuuAnh2016}. \vskip0.2cm \section*{4. Numerical experiment} \vskip0.2cm In this section, we give an example to illustrate the algorithms in this paper. We perform the algorithms by Matlab R2008a running on a PC Desktop with Core(TM) i3CPU M550 3.20GHz with 4GB Ram. \vskip0.2cm \noindent {\bf Example 4.1} Let $H=\mathbb{R}^3$ and $U_1=\{(x_1,x_2,x_3): x_1\in[0,1], x_2\geq 0,x_3\geq 0\}$, $U_2=\{(x_1,x_2,x_3): x_1\geq 0,x_2\in[0,2], x_3\geq 0\}$ and $U_3=\{(x_1,x_2,x_3): x_1\geq 0,x_2\geq 0, x_3\in[0,3]\}$. For each $i=1,2,3$, let $f_i(x,y)=(y_i-x_i)\|x\|$ for all $x=(x_1,x_2,x_3), y=(y_1,y_2,y_3)\in U_i$. From \cite{Wang2018} it follows that each $f_i$ satisfies the conditions (i)-(iv) with the Lipschitz constants $c_1=c_2=1$. Let $V_j=\{(x_1,x_2,x_3): x_1\in\mathbb{R}, 0\leq x_2\leq j,x_3\geq 0\}$ for each $j=1,\ldots,M$. Define the nonexpansive mapping $S_j$ on $V_j$ by $S_jx=(-\frac{x_1}{2}, \frac{x_2^2}{6j},\frac{x_3}{2})$ for $j=1,\ldots,M$. Obviously, $\mathcal{F}=\cap_{i=1}^3 EP(f_i)\cap(\cap_{j=1}^M)Fix(S_j)=\{(0,0,0)\}$. In Algorithm 3.1 and 3.2, put the sequence $\alpha_n=\frac{1}{10}$ and $\alpha_n=\frac{1}{n}$, respectively and put $\rho=\frac{1}{4}$ and $\beta_n= 0.8(1-0.8 e^{-\frac{n}{10}})$ in Algorithm 3.1 and 3.2. According to Theorem 3.1 and 3.2, the sequence $\{x_n\}$ generated by Algorithm 3.1 and 3.2 will converge to the element $x^*=P_{\mathcal{F}}x_1=(0,0,0)$. We will stop the program if $\|x_n\|<10^{-4}$. The following figures show the convergence of Algorithm 3.1 and 3.2 with the different initial point. \begin{figure}[h] \centering \subfloat {% \includegraphics[width=5.2in,totalheight=3.9in]{a1.eps}}\ \caption{ Convergence of Algorithm 3.1 and 3.2 with initial point $x_1=(3,2,10)$} \end{figure} \iffalse \section*{Acknowledgments} \vskip0.2cm This work is supported by Natural Science Foundation of Hebei Province (N0. 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Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000. \end{thebibliography} \end{document} ``` 希望![](https://wenda.latexstudio.net/data/attach/191005/GdXbA2ep.png)插入的图片在参考文献和The following figures show the 。。之间,也就是图片1中黑色箭头位置,但编译完后却出现在图2位置, 代码处已经添加了参数h了。图a1.esp 不知道怎么上传。只上传了图1和2![](https://wenda.latexstudio.net/data/attach/191005/UUgrgOon.png)
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你的那个位置放不下图片才浮动的. 你可以缩小图片, 适配空余的空间就好了.

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