\documentclass[a4paper,12pt,fleqn]{book}
  \usepackage{fmultico}\usepackage{amsmath}\usepackage{mathrsfs}\usepackage{setspace}\usepackage{amssymb}\usepackage{setspace}
  \usepackage{amsthm}\usepackage{fancybox}\usepackage{fancyhdr}\usepackage{graphicx}
  \usepackage[all]{xy}\usepackage{makeidx}\usepackage{xecolour}\usepackage{xepersian}
  \settextfont[Scale=1]{XB Zar}
  \setlatintextfont[Scale=1]{Times New Roman}
  \setdigitfont[Scale=1]{XB Zar}
  \doublespacing
  \pagestyle{empty}
\begin{document}
 $$
\phi :\mathop{A \longrightarrow G'}_{\quad  \:a\: \mapsto [a,x], \; \forall a \in A} 
 $$
 %%%%%%%%%%%
  $$
\phi :\mathop{A \longrightarrow G'}_{\quad  \:a\: \longmapsto [a,x], \; \forall a \in A} 
 $$
%%%%%%%%%%%%%
  $$
\phi \!:\!\!\!\!\!\!\!\mathop{A \longrightarrow G'}_{\quad  \:a\: \longmapsto [a,x], \; \forall a \in A} 
 $$
   $$
\phi \!: \hspace{-5mm} \mathop{A \longrightarrow G'}_{\quad  \:a\: \longmapsto [a,x], \; \forall a \in A} 
 $$
\end{document}