\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw (-6,0) -- (6,0) ; %edit here for the axis
\foreach \x/\y in {-6/{$U(X-2h,f)$},-3/{$U(X-h,f)$},0/{$U(X,f)$},3/{$U(X+h,f)$},6/{$U(X+2h,f)$}} % edit here for the vertical lines
\draw[shift={(\x,0)},color=black] (0pt,3pt) -- (0pt,-3pt)node[below] {\y};
\foreach \x/\y in {-6/-3,-3/0,0/3,3/6}
\draw[bend left,looseness=1.4, shorten >=4pt,shorten <=4pt, blue, thick](\x,0)to node[ label=90: 1/2]{}(\y,0);
\end{tikzpicture}
\end{document}