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\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
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\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
\textcolor{green}{J. Nonlinear  Sci. Appl. 0 (0000), no. 0, 00--00}\\
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{\footnotesize \textcolor{red}{\textsc{\textbf{\large{T}}he
\textbf{\large{J}}ournal of \textbf{\large{N}}onlinear
\textbf{\large{S}}ciences \text{and}
\textbf{\large{A}}pplications}}\\
%ISSN: 1110-111x (electronic)\\
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\title[Short Title]{Title of Paper}

\author[F. Author, S. Author]{First Author$^1$ and Second Author$^2$$^{*}$}

\address{$^{1}$ Department of Mathematics, Shomal University, P. O. Box 731, Amol, Iran.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{first@shomal.ac.ir}}

\address{$^{2}$ Department of Mathematics, Shomal University, P. O. Box 731, Amol, Iran.;
\newline
Amirkabir University}
\email{\textcolor[rgb]{0.00,0.00,0.84}{second@shomal.ac.ir}}

\dedicatory{This paper is dedicated to Professor ABCD}

\subjclass[2000]{Primary 39B82; Secondary 44B20, 46C05.}

\keywords{Convexity, Stability, functional equation, Hahn-Banach
theorem.}

\date{Received: 2 March 2006; Revised: 15 August 15.
\newline \indent $^{*}$ Corresponding author}

\begin{abstract}
The abstract should be informative, precise and not exceed 150
words.
\end{abstract} \maketitle

\section{Introduction and preliminaries}

\noindent Here you should state the introduction, preliminaries and
your notation. Authors are required to state clearly the
contribution of the paper and its significance in the introduction.
There should be some survey of relevant literature.

\subsection{Instructions for author(s)}

Manuscripts should be typeset in English with double spacing by
using AMS-LaTex. The authors are encouraged to use the TJNSA

The abstract should not exceed 150 words. The authors should include
as footnotes for the first page, Keywords and Phrases as well as
2000 Mathematics Subject Classifications. Other footnotes may also
be included in the first page about supporting grants,
presentations, etc. `References' should be listed in alphabetical
order according to the surnames of the first author at the end of
the paper and should be cited in the text as, \cite{M-M, RAS} or
\cite[Theorem 4.1]{MUR}.

\section{Main results}

The following is an example of a definition.

\begin{definition} Let ${\mathcal X}$ be a real or complex linear space. A mapping
$\| \cdot \| :{\mathcal X}\rightarrow \left[ 0,\infty \right) $ is
called a $2$-norm on ${\mathcal X}$\ if it satisfies the following
conditions:

\begin{enumerate}
\item $\| x\| =0\Leftrightarrow x=0,$

\item $\| \lambda x\| =\| \lambda \|
\| x\| \ \ $for all $x\in {\mathcal X}$ and all scalar $\lambda ,$

\item $\| x+y\| ^{2}\leq 2\left( \|
x\| ^{2}+\| y\| ^{2}\right) \ $for all $x,y\in {\mathcal X}.$
\end{enumerate}
\end{definition}

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Here is an example of a table.

\begin{table}[ht]
\caption{}\label{eqtable}
\renewcommand\arraystretch{1.5}
\noindent\[
\begin{array}{|c|c|c|}
\hline
1&2&3\\
\hline f(x)&g(x)&h(x)\\
\hline a&b&c\\
\hline
\end{array}
\]
\end{table}

The following is an example of an example.

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\begin{example} Let ${\mathcal A}$ be a unital algebra, let $a_{0}$ be a
central element of ${\mathcal A}$ with $a_{0}^{n}=a_{0}$ for some
natural number $n$, and let $\theta:{\mathcal A}\to {\mathcal A}$ be
a homomorphism. Define $\varphi:{\mathcal A}\to {\mathcal A}$ by
$\varphi(a)=a_{0}\theta(a)$. Then we have
\begin{eqnarray*}
\varphi(a_{1}\ldots a_{n})&=&a_{0}\theta(a_{1}\ldots a_{n})\\
&=& a_{0}^{n}\theta(a_{1})\ldots\theta(a_{n})\\
&=& a_{0}\theta(a_{1})\ldots a_{0}\theta(a_{n})\\
&=& \varphi(a_{1})\ldots\varphi(a_{n}).
\end{eqnarray*}
Hence $\varphi$ is an $n$-homomorphism.
\end{example}

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The following is an example of a theorem and a proof.

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\begin{theorem}\label{main}
If ${\bf B}$ is an open ball of a real inner product space
${\mathcal X}$ of dimension greater than $1$, ${\mathcal Y}$ is a
real sequentially complete linear topological space, and $f: {\bf
B}\setminus\{0\} \to {\mathcal Y}$ is orthogonally generalized
Jensen mapping with parameters $s=t>\frac{1}{\sqrt{2}} \, r$, then
there exist additive mappings $T: {\mathcal X}\to {\mathcal Y}$ and
$b:{\mathbb R}_+\to {\mathcal Y}$ such that $f(x) = T(x) + b\left
(\|x\|^2\right )$ for all $x\in {\bf B}\setminus \{0\}$.
\end{theorem}

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\begin{proof}
First note that if $f$ is a generalized Jensen mapping with
parameters $t=s \geq r $, then
\begin{eqnarray}\label{additive}
\begin{split}
f(\lambda(x+y))&=\lambda f(x) + \lambda f(y)\\
&\leq \lambda (f(x) + f(y))\\
&= f(x) + f(y)
\end{split}
\end{eqnarray}
for some $\lambda \geq 1$ and all $x, y\in {\bf B}\setminus \{0\}$
such that $x \perp y$.

\medskip
\noindent \underline{\rm Step (I)- the case that f is odd:} Let $x
\in {\bf B} \setminus \{0\}$. There exists $y_0 \in {\bf B}
\setminus \{0\}$ such that $x \perp y_0$, $x + y_0 \perp x - y_0$.
We have
\begin{eqnarray*}
f(x)&=& f(x)- \lambda\, f\left ( \frac{x+y_0}{2\, \lambda}\, \right
) -
\lambda \, f\left ( \frac{x-y_0}{2\, \lambda}\, \right )\\
&&+ \, \lambda \, f\left ( \frac{x+y_0}{2\, \lambda}\, \right ) -
\lambda^2\, f\left ( \frac{x}{2\, \lambda^2}\, \right ) - \lambda^2
\, f\left (
\frac{y_0}{2\, \lambda^2}\, \right )\\
&&+ \, \lambda \, f\left ( \frac{x-y_0}{2\, \lambda}\, \right ) -
\lambda^2 f\left ( \frac{x}{2\, \lambda^2}\, \right ) - \lambda^2\,
f\left (
\frac{-y_0}{2\, \lambda^2}\, \right )\\
&&+\, 2\, \lambda^2 \, f\left (\frac{x}{2\, \lambda^2}\, \right )\\
&=& 2\, \lambda^2 \, f\left ( \frac{x}{2\, \lambda^2}\, \right ).
\end{eqnarray*}

\medskip
\noindent \underline{\rm Step (II)- the case that f is even:} Using
the same notation and the same reasoning as in the proof of Theorem
\ref{main}, one can show that $f(x)=f(y_0)$ and the mapping $Q:
{\mathcal X}\to {\mathcal Y}$ defined by $Q(x) : = (4\lambda^2)^n
f((2\lambda^2)^{-n}x)$ is even orthogonally additive.

\medskip
Now the result can be deduced from Steps (I) and (II) and
(\ref{additive}).
\end{proof}

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The following is an example of a remark.

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\begin{remark}
One can easily conclude that $g$ is continuous by using Theorem
\ref{main}.
\end{remark}

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{\bf Acknowledgements:} Acknowledgements could be placed at the end
of the text but precede the references.

\bibliographystyle{amsplain}
\begin{thebibliography}{10}

\bibitem{MUR} G.J. Murphy, \textit{$C^*$-Algebras and Operator Theory}, Academic Press, Boston, 1990.

\bibitem{M-M} M. Mirzavaziri and M.S. Moslehian, \textit{Automatic continuity of $\sigma$-derivations in
$C^*$-algebras}, Proc. Amer. Math. Soc. \textbf{134} (2006),
3319--3327.

\bibitem{RAS} Th.M. Rassias, \textit{Stability of the generalized orthogonality functional equation},
Inner product spaces and applications, 219--240, Pitman Res. Notes
Math. Ser., 376, Longman, Harlow, 1997.

\end{thebibliography}

\end{document}

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