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\noindent\parbox{2.95cm}{\includegraphics*[keepaspectratio=true,scale=0.125]{AFA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
\qquad Ann. Funct. Anal. 2 (2011), no. 2, 22--33\\
{\footnotesize
\qquad \textsc{\textbf{$\mathscr{A}$}nnals of \textbf{$\mathscr{F}$}unctional
\textbf{$\mathscr{A}$}nalysis}\\
\qquad ISSN: 2008-8752 (electronic)\\
\qquad URL: \textcolor[rgb]{0.00,0.00,0.99}{www.emis.de/journals/AFA/}
}\\[.5in]}

\title[Geometric constants of $\Bbb R^2$]{Some geometric constants of absolute normalized norms on $\Bbb R^2$}

\author[H. Mizuguchi, K.-S. Saito]{Hiroyasu Mizuguchi and Kichi-Suke Saito$^{*}$}

\address{Department of Mathematical Sciences, Graduate School of Science and Technology, Niigata University,
Niigata, 950-2181 Japan.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{mizuguchi@m.sc.niigata-u.ac.jp}}
\email{\textcolor[rgb]{0.00,0.00,0.84}{saito@math.sc.niigata-u.ac.jp}}

\dedicatory{{\rm Communicated by J. I. Fujii}}

\subjclass[2010]{Primary 46B20; Secondary 46B25.}

\keywords{ Zb{\rm \u{a}}ganu constant, absolute norm, von
Neumann-Jordan constant.}

\date{Received: 31 March 2011; Accepted: 14 June 2011.
\newline \indent $^{*}$ Corresponding author}

\begin{abstract} We consider the Banach space $X=(\Bbb R^2, \|\cdot\|)$ with a normalized, absolute norm.
Our aim in this paper is to calculate the modified Neumann-Jordan constant $C'_{NJ}(X)$ and the Zb{\rm \u{a}}ganu constant $C_Z(X)$.
\end{abstract} \maketitle
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