Using LaTeX expression in gnuplot I am having difficulty to get $\bar u$ (to denote average of values $u_i$) as label for the x-axis in the output eps figure.
Any help would be appreciated!
Many thanks! 
 A: I have not tried the following, but they might work for you*
You could try the Baltic letter ū (u with macron) either directly or with Unicode U+016B or html &#363;
Or you could follow the advice here, which seems to imply that something like 
set xlabel "$\bar{u}$"

might work.
A: If your penultimate goal is to embed your plot in a Latex document, you might consider using the gnuplottex package (as an alternative to pgfplots which is an awesome package). The idea is rather simple: you write your code chunk in your tex document directly (like you would do with Sweave), et voilà!
Here is an example (grabbed from gnuplot demos):
\documentclass{standalone}
\usepackage{gnuplottex}

\begin{document}
\begin{gnuplot}[scale=0.95, terminal=epslatex]
set style fill transparent pattern 4 bo
set style function filledcurves y1=0
set clip two    
Gauss(x,mu,sigma) = 1./(sigma*sqrt(2*pi)) * exp( -(x-mu)**2 / (2*sigma**2) )
d1(x) = Gauss(x, 0.5, 0.5)
d2(x) = Gauss(x,  2.,  1.)
d3(x) = Gauss(x, -1.,  2.)
set xrange [-5:5]
set yrange [0:1]
set xlabel "$\\bar x$ values"
unset colorbox    
plot d1(x) fs solid 1.0 lc rgb "forest-green", \
     d2(x) lc rgb "gold", d3(x) lc rgb "red"
\end{gnuplot}
\end{document}

You'll need to compile with the -shell-escape option to pdflatex.

