To have LaTeX place some material below below the string "max", simply use the macro \max_{...}
: If you're in displaymath mode (which you will be if you're in an environment such as equation
), this will result in the argument of the \max
command being placed below (rather than in a subscript position) the string "max".
Separately, I would recommend that you typeset the strings "rank", "pred", and "succ" in upright-roman characters since they denote math "operators". One way to do this is to load the amsmath
package and use its \DeclareMathOperator
instruction to define the corresponding macros \rank
, \pred
, and \succ
. Aside: Because the macro \succ
already exists -- and creates a math symbol that looks like a curvy >
sign -- it has to be undefined first before it can be redefined as a math operator. Obviously, if you need to use the original meaning of \succ
elsewhere in your document, you should not redefine it to act as a math operator; instead, devise a new macro name, e.g., \succeeds
.
Furthermore, I would use the \bar
instruction to create lines above the "c" and "w" characters. Doing so creates horizontal lines that aren't quite as "heavy" as those produced by \overline
.

\documentclass{article}
\usepackage{amsmath} % for \DeclareOperator macro and align environment
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\pred}{pred}
\let\succ\relax % undefine \succ first
\DeclareMathOperator{\succ}{succ} % now redefine it as an "operator"
\begin{document}
\begin{align*}
\rank_u(n_i)&=\bar{w}_i + \max_{n_j\in\succ(n_i)}
\bigl(\bar{c}_{i,j}+\rank_u(n_j)\bigr)\\
\rank_d(n_i)&=\bar{w}_i + \max_{n_j\in\pred(n_i)}
\bigl\{ \rank_d(n_j)+\bar{w}_j+\bar{c}_{j,i}\bigr\}
\end{align*}
\end{document}