Math equation in latex

Question

hello how can I write this equation in latex?

Answer 1

Here are two ways to typeset the equation in question. The first replicates the expression in the screenshot you posted. The second uses what I would consider to be a somewhat more standard way of expressing the idea that the minimization takes place over an index k that belongs to the set of integers ranging from 1 to n.

\documentclass{article} % or some other suitable document class
\usepackage{amsmath}    % for 'align*' environment
\usepackage{newtxtext,newtxmath} % optional (Times roman fonts)

\begin{document}
\begin{align*}
AB[i,j] &= \min\limits_{k=1}^n (A[i,k]+B[k,j])  \\
AB[i,j] &= \min\limits_{k\in\{1,\dots,n\}} (A[i,k]+B[k,j])
\end{align*}
\end{document} 

Answer 2

An alternative for \min\limits_{k=1}^n using \DeclareMathOperator*{\mlimi}{\min}.

\documentclass[12pt]{article}
\usepackage{newtxtext,newtxmath}
\DeclareMathOperator*{\mlimi}{\min}
\begin{document}
\[AB[i,j]=\mlimi_{k=1}^n (A[i,k]+B[k,j])\]
\end{document}

It is possible to adjiust (decreasing) the upper and lower limits using \scriptscriptstyle.

\documentclass[12pt]{article}
\usepackage{newtxtext,newtxmath}
\DeclareMathOperator*{\mlimi}{\min}
\begin{document}
\[AB[i,j]=\mlimi_{\scriptscriptstyle k=1}^{\scriptscriptstyle n} (A[i,k]+B[k,j])\]
\end{document}