can somebody help me write my equation like the image given below

Question

\begin{equation}
 f (u_p) = f(x)={(f(u_i ),                 d(u_p,u_i)=0 
 argmax_{v \in V} \sum{i=1}^{k} wD(v,f(u_i )) ,& otherwise )}  (5)
\end{equation}

Answer 1

You should use the cases environment.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
    \begin{align}
      f(u_p) = f(x)= 
      \begin{cases}
        f(u_i),& d(u_p,u_i)=0 \
        \arg\max_{v \in V} \sum_{i=1}^{k} wD(v,f(u_i )), & \textit{otherwise} 
      \end{cases}
    \end{align}
\end{document}

yields

Answer 2

You don't really want to replicate the mistakes, such as the italic “max” and ”otherwise”.

Here are two possibilities, the latter replicates the alignment in the picture using array.

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator*{\argmax}{arg,max}
\begin{document}
\begin{equation}
f (u_p) = f(x)=
\begin{cases}
  f(u_i), & d(u_p,u_i)=0 \
  \argmax_{v \in V} \sum_{i=1}^{k} wD(v,f(u_i)), & \text{otherwise}
\end{cases}
\end{equation}
Alternative, like in the picture
\begin{equation}
f (u_p) = f(x)=
\left{
\begin{array}{@{}l@{}}
  f(u_i), \hfill d(u_p,u_i)=0 \[1ex]
  \argmax_{v \in V} \sum_{i=1}^{k} wD(v,f(u_i)), \quad\text{otherwise}
\end{array}
\right.
\end{equation}
\end{document}