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\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{conjecture}[theorem]{Conjecture}
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%-------------------------- Pleased do not change the following line-------------------------------------------
\noindent \textcolor[rgb]{0.99,0.00,0.00}{This is a submission to one of journals of TMRG: BJMA/AFA}\\[.5in]
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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, National Institute of Technology,
Jalandhar 144011, Punjab, India.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{first1@afa.ac.ir;
first2@afa.ac.ir}}

\address{$^{2}$ Department of Mathematics, Ferdowsi University, P. O. Box 1159, Mashhad 91775, Iran;
\newline
Tusi Mathematical Research Group (TMRG), Mashhad, Iran.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{second@banach.ac.ir}}

%\dedicatory{This paper3 is dedicated to Professor ABCD}

\subjclass[2010]{Primary 39B82; Secondary 44B20, 46C05.}

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

\date{Received: xxxxxx; Revised: yyyyyy; Accepted: zzzzzz.
\newline \indent $^{*}$ Corresponding author}

\begin{abstract}
The BJMA is an author-prepared journal which means that authors are
responsible for the proper formatting of accepted manuscripts by
using the style file of the BJMA.
\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 BJMA style
file that has been developed for LaTeX2e standard and can be found
at journal website
\begin{center}
`http://www.emis.de/journals/BJMA/'.
\end{center}

While you are preparing your paper, please take care of the following:
\begin{enumerate}
\item Abstract: 200 words or less.\\
\item MSC2010: Primary only one item; and Secondary at least one item.\\
\item Key words: At least 3 items and at most 5 items.\\
\item Authors: Full names, mailing addresses and emails of all authors.\\
\item Margins: A long formula should be broken into two or more lines. Empty spaces in the text should be removed.\\
\item Tags (Formula Numbers): Use \label{A} and \eqref{A}. Remove unused tags.\\
\item Acknowledgement: At the end of paper but preceding to References.\\
\item References: Use \cite{M-M} to refer to the specific book/paper [2] in the text. Remove unused references. References should be listed in the alphabetical order according to the surnames of the first author at the end of the paper and should be cited in the text as, e.g., [2] or [3, Theorem 4.2], etc.\\
\item Abbreviations: Abbreviations of titles of periodicals/books should be given by using Math. Reviews, see Abbreviations of names of serials or MRLookup.

\end{enumerate}

\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}

%---------------------------------------------------------------------------------------%

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}

This is an example of a matrix
\begin{equation*}
\begin{bmatrix}
1 & -2 \\
3 &  5
\end{bmatrix} \qquad
\begin{vmatrix}
5 &  2\\
0 & 3
\end{vmatrix} \qquad
\begin{Vmatrix}
5 &  2\\
0 & 3
\end{Vmatrix}
\end{equation*}

The following is an example of an example.

%---------------------------------------------------------------------------------------%

\begin{example} 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}\label{2.1}
\varphi(a_{1}\ldots a_{n})&=&a_{0}\theta(a_{1}\ldots a_{n})\nonumber\\
&=& a_{0}^{n}\theta(a_{1})\ldots\theta(a_{n})\nonumber\\
&=& a_{0}\theta(a_{1})\ldots a_{0}\theta(a_{n})\nonumber\\
&=& \varphi(a_{1})\ldots\varphi(a_{n}).
\end{eqnarray}
Hence $\varphi$ is an $n$-homomorphism.
\end{example}

%---------------------------------------------------------------------------------------%

The following is an example of a theorem and a proof. Please note
how to refer to a formula.

%---------------------------------------------------------------------------------------%

\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}

%---------------------------------------------------------------------------------------%

\begin{proof}
First note that if $f$ is a generalized Jensen mapping with
parameters $t=s \geq r $, then

\begin{align}\label{additive}
f(\lambda(x+y))&=\lambda f(x) + \lambda f(y)\nonumber\\
&\leq \lambda (f(x) + f(y))\nonumber\\
&= f(x) + f(y)
\end{align}

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
\eqref{additive}.
\end{proof}

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The following is an example of a remark.

%---------------------------------------------------------------------------------------%

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

%---------------------------------------------------------------------------------------%

Again, note how we refer to Theorem \ref{main} and formula
\eqref{2.1}.
\\
\\
{\bf Acknowledgement.} Acknowledgements could be placed at the end
of the text but precede the references.


\bibliographystyle{amsplain}
\begin{thebibliography}{99}

\bibitem{haag1} U. Haagerup, \textit{Solution of the similarity problem for cylic representations
of $C^*$-algebras}, Ann. of Math. (2) {\bf 118} (1983), no. 2,
215--240.

\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), no. 11,
3319--3327.

\bibitem{H} M.S. Moslehian, \textit{Ky Fan inequalities}, Linear Multilinear Algebra (to appear).

\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.

\bibitem{JV82} J.P. Vial, \textit{Strong  convexity of set and functions}, J. Math. Econom \textbf{9} (1982), no. 1-2, 187--205.


\end{thebibliography}

\end{document}

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