%------------------------------------------------------------------------------ % Here please write the date of submission of paper or its revisions: %------------------------------------------------------------------------------ % \documentclass[12pt, reqno]{amsart} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} \textheight 22.5truecm \textwidth 14.5truecm \setlength{\oddsidemargin}{0.35in}\setlength{\evensidemargin}{0.35in} \setlength{\topmargin}{-.5cm} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{summary}[theorem]{Summary} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{problem}[theorem]{Problem} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \numberwithin{equation}{section} \begin{document} \setcounter{page}{1} \title[Short Title]{Title of Paper} \author[F. Author, S. Author]{First Author$^1$ and Second Author$^2$$^{*}$} \address{$^{1}$ Department of Mathematics, University of AAAA, BBBB 654321, CCCC, India.} \email{\textcolor[rgb]{0.00,0.00,0.84}{first1@afa.ac.ir; first2@afa.ac.ir}} \address{$^{2}$ Department of Pure 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@afa.ac.ir}} %\dedicatory{This paper 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 journal 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 journal. The journal does not consider any more submission of (co)authors while one of their papers is \textbf{still under review by the journal}. \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 journal style file that has been developed for LaTeX2e standard and can be found at the website of the journa. While you are preparing your paper, please take care of the following: \begin{enumerate} \item Abstract: 200 words or less with no reference number therein.\\ \item MSC2010: Primary only one item; and Secondary at least one item (We need at least one in MSC46 or MSC47). \\ \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 $\backslash label\{A\}$ and $\backslash eqref\{A\}$. Remove unused tags. \\ \item Acknowledgement: At the end of paper but preceding to References.\\ \item References: Use $\backslash cite\{MM\}$ to refer to the specific book/paper [2] (with $\backslash bibitem~\{MM\}$) 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} \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\\ &=& \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 $x \perp y$. Now the result can be deduced from \eqref{additive}. \end{proof} %---------------------------------------------------------------------------------------% 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{MM} 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, arXiv:1108.1467v2 (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} %------------------------------------------------------------------------------ % End of journal.tex %------------------------------------------------------------------------------