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\begin{document}

\title{\vspace{-1in}%
\parbox{\linewidth}{\footnotesize\noindent
\textbf{Applied Mathematics E-Notes, xx(20xx), xx-xx} \copyright \hfill ISSN 1607-2510
\newline
Available free at mirror sites of http://www.math.nthu.edu.tw/$\sim$amen/} 
\vspace{0pt} \\
Title\thanks{%
Mathematics Subject Classifications: 20F05, 20F10, 20F55, 68Q42.}}
\date{{\small Received 20 July 2000}}
\author{First Second Family\thanks{%
Department of Mathematics, Binzhou Normal College, Binzhou, Shandong 256604,
P. R. China}\ , Sui Sun Cheng\thanks{%
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, R.
O. China}\ , Tzon Tzer Lu\thanks{%
Department of Applied Mathematics, Sun Yat-sen Univeristy, Kaohsiung, Taiwan
80424, R. O. China}}
\maketitle

\begin{abstract}
Solutions of the form $x(z)=\lambda z^{\mu }$ are found for the iterative
functional differential equation $x^{(n)}(z)=\left( x\left( x\left(
...x\left( z\right) \right) \right) \right) ^{k}.$
\end{abstract}

\section{Introduction}

The basic idea is that a short note should be presented in a simple manner.
Therefore, use simple notations, symbols, etc. Displayed equation should be
labeled in the following format 
\begin{equation}
x(z)=\lambda z^{\mu },  \label{1}
\end{equation}
\begin{equation}
x^{(n)}(z)=\left( x^{[m]}(z)\right) ^{k}.  \label{2}
\end{equation}

Lemmas, Theorems, and Corollaries should be typed such as the following:

\smallskip

\begin{theorem}
Let $\Omega $ be a domain of the complex plane $C$ which does not include
the negative real axis (nor the origin). Then there exist $m$ distinct
(single valued and analytic) power functions of the form (\ref{1}) which are
solutions of (\ref{2}).
\end{theorem}

\smallskip

Proofs should be typed as follows:

\smallskip

\begin{proof}
We remark that each solution $x_{i}(z)=\lambda _{i}z^{\mu _{i}}$ has a
nontrivial fixed point $\alpha _{i}$. Indeed, from $\lambda _{i}\alpha
_{i}^{\mu _{i}}=\alpha _{i},$ we find 
\begin{equation*}
\alpha _{i}=\lambda _{i}^{1/(1-\mu _{i})}=\left[ \mu _{i}(\mu _{i}-1)\cdot
\cdot \cdot (\mu _{i}-n+1)\right] ^{1/(k+n-1)}\neq 0,
\end{equation*}%
etc. ...
\end{proof}

\smallskip

Other texts can be typed such as the following: As an example, consider the
equation 
\begin{equation*}
x^{\prime }(z)=x(x(z)).
\end{equation*}%
From 
\begin{equation*}
\mu ^{2}-\mu +1=0,
\end{equation*}%
we find roots $\mu _{\pm }=(1-\sqrt{3}i)/2.$ We find $\lambda _{-}=\mu
_{-}^{1/\mu _{-}}\approx 2.145-1.238i,$ $\lambda _{+}=\mu _{+}^{1/\mu
_{+}}\approx 2.145+1.238i.$ Since $\left\vert \mu _{\pm }\right\vert =1$ and 
$\mu _{\pm }^{6}=1,$ they are roots of unity. This shows that the
requirements in the main Theorem in \cite{r1} does not hold. Therefore, we
have found analytic solutions which cannot be guaranteed by the main Theorem
in \cite{r1}. 

\smallskip

\begin{remark}
A figure should be prepared in a separate EPS or JPG or BMP file and placed
at the center by appropriate TEX commands.
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\smallskip

\textbf{Acknowledgment.} Statements can be placed here.

\smallskip

References should be typed as follows:

\begin{thebibliography}{9}
\bibitem{r1} J. G. Si, W. R. Li and S. S. Cheng, Analytic solutions of an
iterative functional differential equation, Comput. Math. Appl.,
33(1997), 47--51.

\bibitem{r2} E. Eder, The functional differential equation $x^{\prime
}(t)=x(x(t)),$ J. Differential Equations , 54(1984), 390--400.

\bibitem{r3} L. W. Griffiths, Introduction to the Theory of Equations, 2$%
^{nd}$ ed., Wiley, New York, 1947.
\end{thebibliography}

\end{document}
