I have a long equation but long enough to occupy two lines. I want to break it to improve readability. How can I break it?

Question

\begin{eqnarray}
\lim_{n\rightarrow +\infty }d(SAx_n,A^{2}x_n) \leq \frac{1}{3}\left[ \lim_{n\rightarrow +\infty }d(SAx_n,St)+\lim_{n\rightarrow +\infty }d(St,S^{2}x_n) 
+ \lim_{n\rightarrow +\infty }d(St,S^{2}x_n)\right]. \notag
\end{eqnarray}

Answer 1

Here are 4 possibilities. Note this particular equation fits in a singleline if you have sensible margins (i.e. if you don't use margin notes). Also, eqnarray shouldn't be used anymore, as it leads to bad spacing. Use one of the amsmath environment instead.

\documentclass[11pt]{article}
\usepackage{showframe}
\renewcommand{\ShowFrameLinethickness}{0.3pt}
\usepackage{mathtools}

\begin{document}

\begin{align*}
\lim_{n\rightarrow +\infty }d(SAx_n,A^{2}x_n) \leq \frac{1}{3}\Bigl[ & \lim_{n\rightarrow +\infty }d(SAx_n,St)
 \\ + & \lim_{n\rightarrow +\infty }d(St,S^{2}x_n)
  + \lim_{n\rightarrow +\infty }d(St,S^{2}x_n)\Bigr].
\end{align*}
\bigskip

\begin{align*}
\lim_{n\rightarrow +\infty }d(SAx_n,A^{2}x_n) \leq \frac{1}{3}\Bigl[ \lim_{n\rightarrow +\infty }d(SAx_n,St)
 & +\lim_{n\rightarrow +\infty }d(St,S^{2}x_n) \\
 & + \lim_{n\rightarrow +\infty }d(St,S^{2}x_n)\Bigr].
\end{align*}
\bigskip

\begin{flalign*}
   & \mathrlap{\lim_{n\rightarrow +\infty }d(SAx_n,A^{2}x_n) \leq} \\
  & & \frac{1}{3}\Bigl[ & \lim_{n\rightarrow +\infty }d(SAx_n,St)
  +\lim_{n\rightarrow +\infty }d(St,S^{2}x_n) + \lim_{n\rightarrow +\infty }d(St,S^{2}x_n)\Bigr].
\end{flalign*}
\bigskip
\begin{align*}
   & \lim_{n\rightarrow +\infty }d(SAx_n,A^{2}x_n) \leq \\
  \frac{1}{3}\Bigl[ &\lim_{n\rightarrow +\infty }d(SAx_n,St)
  +\lim_{n\rightarrow +\infty }d(St,S^{2}x_n) + \lim_{n\rightarrow +\infty }d(St,S^{2}x_n)\Bigr].
\end{align*}

\end{document}