%------------------------------------------------------------------------------ % Beginning of journal.tex %------------------------------------------------------------------------------ % \documentclass[12pt, reqno]{amsart} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, color} \usepackage{latexsym} \usepackage[bookmarksnumbered, plainpages]{hyperref} \textheight 22.5truecm \textwidth 14.5truecm \setlength{\oddsidemargin}{0.35in}\setlength{\evensidemargin}{0.35in} \setlength{\topmargin}{-.5cm} \newcommand{\R}{{\mathbb R}} \newcommand{\N}{{\mathbb N}} \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{xca}[theorem]{Exercise} \newtheorem{problem}[theorem]{Problem} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \numberwithin{equation}{section} \newtheorem{thm}{Theorem}[section] \newtheorem{cor}[thm]{Corollary} \newtheorem{lem}[thm]{Lemma} \newtheorem{prop}[thm]{Proposition} \theoremstyle{definition} \newtheorem{defn}[thm]{Definition} \theoremstyle{remark} \newtheorem{rem}[thm]{Remark} % \newtheorem*{ex}{Example} \newtheorem{ex}{Example} \numberwithin{equation}{section} %%%%%%%%%%%%% THE AUTHORS' OWN MACROS \newcommand{\zit}[1]{\textup{(\ref{#1})}} \newcommand{\rez}[1]{\frac{1}{{#1}}} \newcommand{\ri}{\right} \newcommand{\li}{\left} \newcommand{\D}{\displaystyle} \newcommand{\di}{\mathrm{d}} \newcommand{\abs}[1]{\li|{#1}\ri|} \newcommand{\B}[1]{\mbox{\boldmath$#1$}} \newcommand{\Bi}[1]{\mbox{\scriptsize\boldmath$#1$}} \newcommand{\Bii}[1]{\mbox{\tiny\boldmath$#1$}} \newcommand{\dosu}{\sum_{{\scriptstyle\Bi{\alpha}\inn_0^{d+1}}\atop{\scriptstyle\abs{\Bi{\alpha}}=n}}}% \newcommand{\nor}[1]{\|{#1}\|} \newcommand{\inn}{\in\mathbb{N}} \newcommand{\PN}[1]{\li\bracevert\strut\!#1\!\ri\bracevert} %\newcommand{\R}{\mathbb{R}} \newcommand{\ve}{\varepsilon} \newcommand{\bgl}[1]{\begin{equation}\label{#1}} \newcommand{\egl}{\end{equation}} \def\id{\hbox{{\rm id}}} \begin{document} \setcounter{page}{121} \noindent\parbox{2.85cm}{\includegraphics*[keepaspectratio=true,scale=1.75]{BJMA.jpg}} \noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent Banach J. Math. Anal. 2 (2008), no. 2, 121--128\\ $\frac{\rule{4.55in}{0.05in}}{{}}$\\ {\footnotesize \textcolor[rgb]{0.65,0.00,0.95}{\textsc{\textbf{\large{B}}anach \textbf{\large{J}}ournal of \textbf{\large{M}}athematical \textbf{\large{A}}nalysis}}\\ ISSN: 1735-8787 (electronic)\\ \textcolor[rgb]{0.00,0.00,0.84}{\textbf{http://www.math-analysis.org }}\\ $\frac{{}}{\rule{4.55in}{0.05in}}$}\\[.5in]} \title[Korovkin-type theorems]{ Two Korovkin-type theorems in multivariate approximation} \author[A. Guessab, G. Schmeisser]{Allal Guessab$^1$$^{*}$ and Gerhard Schmeisser$^2$} \address{$^{1}$ Department of Applied Mathematics, University of Pau, 64000 Pau, France.} \email{\textcolor[rgb]{0.00,0.00,0.84}{allal.guessab@univ-pau.fr}} \address{$^{2}$ Department of Mathematics, University of Erlangen-Nuremberg, 91054 Erlangen, Germany.} \email{\textcolor[rgb]{0.00,0.00,0.84}{schmeisser@mi.uni-erlangen.de}} \dedicatory{Dedicated to Professor Josip E.\ Pe\v{c}ari\'c\\ \vspace{.5cm} {\rm Submitted by G. V. Milovanovi\'c}} \subjclass[2000]{Primary 41A36, 41A63; Secondary 26B25.} \keywords{Korovkin-type theorems, Positive linear operators, Convexity.} \date{Received: 30 April 2008; Accepted 23 June 2008. \newline \indent $^{*}$ Corresponding author} \begin{abstract} Let $\Omega$ be a compact convex subset of $\R^d$ and let $(L_n)_{n\in\N}$ be a sequence of positive linear operators that map $C(\Omega)$ into itself. We establish two Korovkin-type theorems in which the limit of the sequence of operators is not necessarily the identity. \end{abstract} \maketitle \vspace{1in} \end{document} .