Pruebas del paquete listings

1 \begin{displaymath}2 \oint_{S}\vec{E}\cdot d\vec{S}=\frac{q}{\

epsilon_{0}}3 \end{displaymath}

∮S

~E · d~S =q

ε0

1 \begin{trivlist}2 \item\input{\jobname.exa}3 \end{trivlist}

Let H be a Hilbert space, C be a closedbounded convex subset of H , T a nonex-pansive self map of C. Suppose that asn → ∞, an,k → 0 for each k, and γn =∑∞

k=0 (an,k+1 − an,k)+ → 0. Then foreach x in C, Anx =

∑∞k=0 an,kT

kx con-verges weakly to a fixed point of T .

The numbered equation

utt−∆u+u5+u |u|p−2 = 0 in R3×[0,∞[(1)

is automatically numbered as equation 2.

Let $H$ be a Hilbert space, $C$ be a closed bounded convex subset of $H$, $T$a nonexpansive self map of $C$. Suppose that as $n\rightarrow\infty$,$a_{n,k}\rightarrow0$ for each $k$, and $\gamma_{n}=\sum_{k=0}ˆ{\infty}\left(a_{n,k+1}-a_{n,k}\right) ˆ{+}\rightarrow0$. Then for each $x$ in $C$,$A_{n}x=\sum_{k=0}ˆ{\infty}a_{n,k}Tˆ{k}x$ converges weakly to a fixed point of$T$ .

The numbered equation\begin{equation}u_{tt}-\Delta u+uˆ{5}+u\left| u\right| ˆ{p-2}=0\text{ in }\mathbf{R}%ˆ{3}\times\left[ 0,\infty\right[ \label{eqn1}%\end{equation}is automatically numbered as equation \ref{eqn1}.

1 Let $H$ be a Hilbert space, $C$ be aclosed bounded convex subset of $H$,$T$

2 a nonexpansive self map of $C$. Supposethat as $n\rightarrow\infty$,

3 $a_{n,k}\rightarrow0$ for each $k$, and$\gamma_{n}=\sum_{k=0}ˆ{\infty}\left(

4 a_{n,k+1}-a_{n,k}\right) ˆ{+}\rightarrow0$. Then for each $x$ in $C$,

5 $A_{n}x=\sum_{k=0}ˆ{\infty}a_{n,k}Tˆ{k}x$converges weakly to a fixed point

of6 $T$ .7

8 The numbered equation9 \begin{equation}

10 u_{tt}-\Delta u+uˆ{5}+u\left| u\right|ˆ{p-2}=0\text{ in }\mathbf{R} %

11 ˆ{3}\times\left[ 0,\infty\right[ \label{eqn1} %

12 \end{equation}13 is automatically numbered as equation \

ref{eqn1}.

Let H be a Hilbert space, C be a closedbounded convex subset of H , T a nonex-pansive self map of C. Suppose that asn → ∞, an,k → 0 for each k, and γn =∑∞

k=0 (an,k+1 − an,k)+ → 0. Then foreach x in C, Anx =

∑∞k=0 an,kT

kx con-verges weakly to a fixed point of T .

The numbered equation

utt−∆u+u5+u |u|p−2 = 0 in R3×[0,∞[(2)

is automatically numbered as equation 2.

1

1 \begin{equation}2 \forall x \in \mathbf{R}:3 \qquad xˆ{2} \geq 04 \end{equation}

∀x ∈ R : x2 ≥ 0 (3)

1 \begin{displaymath}2 xˆ{2} \geq 0\qquad3 \textrm{para todo }x\in\mathbb{R}4 \end{displaymath}

x2 ≥ 0 para todo x ∈ R

Codigo de este archivo

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5

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\begin{document}Pruebas del paquete listings\begin{example}$$\oint_{S}\vec{E}\cdot d\vec{S}=\frac{q}{\epsilon_{0}} $$\end{example}

\begin{lstlisting}[style=L]\begin{trivlist}

\item\input{\jobname.exa}\end{trivlist}

\end{lstlisting}\begin{ejercicio}Let $H$ be a Hilbert space, $C$ be a closed bounded convex subset of $H$, $T$a nonexpansive self map of $C$. Suppose that as $n\rightarrow\infty$,$a_{n,k}\rightarrow0$ for each $k$, and $\gamma_{n}=\sum_{k=0}ˆ{\infty}\left(a_{n,k+1}-a_{n,k}\right) ˆ{+}\rightarrow0$. Then for each $x$ in $C$,$A_{n}x=\sum_{k=0}ˆ{\infty}a_{n,k}Tˆ{k}x$ converges weakly to a fixed point of$T$ .

The numbered equation\begin{equation}u_{tt}-\Delta u+uˆ{5}+u\left| u\right| ˆ{p-2}=0\text{ in }\mathbf{R}%ˆ{3}\times\left[ 0,\infty\right[ \label{eqn1}%\end{equation}is automatically numbered as equation \ref{eqn1}.

6

\end{ejercicio}\begin{example}Let $H$ be a Hilbert space, $C$ be a closed bounded convex subset of $H$, $T$a nonexpansive self map of $C$. Suppose that as $n\rightarrow\infty$,$a_{n,k}\rightarrow0$ for each $k$, and $\gamma_{n}=\sum_{k=0}ˆ{\infty}\left(a_{n,k+1}-a_{n,k}\right) ˆ{+}\rightarrow0$. Then for each $x$ in $C$,$A_{n}x=\sum_{k=0}ˆ{\infty}a_{n,k}Tˆ{k}x$ converges weakly to a fixed point of$T$ .

The numbered equation\begin{equation}u_{tt}-\Delta u+uˆ{5}+u\left| u\right| ˆ{p-2}=0\text{ in }\mathbf{R}%ˆ{3}\times\left[ 0,\infty\right[ \label{eqn1}%\end{equation}is automatically numbered as equation \ref{eqn1}.\end{example}\begin{example}\begin{equation}\forall x \in \mathbf{R}:\qquad xˆ{2} \geq 0\end{equation}\end{example}\begin{example}\begin{displaymath}xˆ{2} \geq 0\qquad\textrm{para todo }x\in\mathbb{R}\end{displaymath}\end{example}

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