I can't make pdf I type this :
$E(\frac{1}{2}\Phi +\frac{1}{2}\Phi\prime ,\frac{1}{2}\Psi +\frac{1}{2}\Psi\prime)\leq \frac{1}{2}E(\Phi , \Psi\prime)+\frac{1}{2}E(\Phi\prime ,\Psi).$
\begin{eqmarray}
$\sum_{u\in\Sigma(0,\Gamma) }\frac{1}{|\Gamma_u | }E_{u,\Phi}(\Psi(u)) $
$~&=&\sum_{u\in \Sigma(0,\Gamma) }\frac{1}{|\Gamma_u| }\sum\underline{v\in\Sigma_u(0) }m((u,v))f(d(\Psi(u),\Phi(v)))$
$~&=&\sum\_{u\in\Sigma(0,\Gamma) }\frac{1}{|\Gamma_u| }\sum_{\eta\in\Sigma(1),u\subset\eta }\frac{m(\eta)}{2}f(d(\Psi(u),\Phi(\eta -u))),$
$~&=&\sum_{\eta\in\Sigma(1,\Gamma) }\frac{m(\eta }{2|\Gamma_\eta | }\sum_{u\in\Sigma(0),u\subset\eta }f(d(\Psi(u),\Phi(\eta -u)))$
$~&=&\sum_{(u,v)\in\Sigma(1,\Gamma) }\frac{m((u,v))}{2|\Gamma_(u,v)| }(f(d(\Psi(u),\Phi(v)))+f(d(\Psi(v),\Phi(u)))$
$~&=&\sum_{(u,v)\in\Sigma(1,\Gamma) }\frac{m((u,v))}{|\Gamma_(u,v) }f(d(\Psi(u),\Phi(v)))$
$~&=&E(\Phi ,\Psi).$
\end{eqmarray}
please help me
eqnarrayinstead ofeqmarray.But in facteqnarrayis not what you should be using.alignis better. See http://tex.stackexchange.com/questions/196/eqnarray-vs-align – Ethan Bolker Jun 30 '15 at 15:07eqnarrayoralignyou should not use$you are already in math mode and you may not have blank lines. But please always post complete documents and say exactly what error you got, so we can reproduce it. – David Carlisle Jun 30 '15 at 15:08