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\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, 31--41 \\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\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 }}\\
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\title[Triangle inequality]{Some remarks on the triangle inequality for norms}

\author[L. Maligranda]{Lech Maligranda}

\address{Department of Mathematics, Lule{\aa} University of Technology, SE--971 87 Lule{\aa}, Sweden.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{lech@sm.luth.se}}


\dedicatory{Dedicated to Professor Josip Pe\v{c}ari\'{c}\\
\vspace{.5cm}{\rm Submitted by D. E. Alspach}}

\subjclass[2000]{Primary 46B20, 46B99; Secondary 51M16.}

\keywords{Inequalities, normed space, norm inequality, triangle
inequality, reversed triangle inequality, angular distance,
Fischer--Musz\'ely equality.}

\date{Received: 11 April 2008; Accepted 24 April 2008.}

\begin{abstract}
Remarks about strengthening of the triangle inequality and its
reverse inequality in normed spaces for two and more elements are
collected. There is also a discussion on Fischer--Musz\'ely equality
for $n$-elements in a normed space. Some other estimates which
follow from the triangle inequality are also presented.
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