documentclass{article}
usepackage{amsmath,amssymb}
newcommand{vertiii}[1]{{leftvertkern-0.25exleftvertkern-0.25exleftvert #1
    rightvertkern-0.25exrightvertkern-0.25exrightvert}}
begin{document}
$vertiii{a}$,
$vertiii{int_0^1 a(x),mathrm{d}x}$,
$displaystyle vertiii{int_0^1 a(x),mathrm{d}x}_vertiii{b}$

$lVert a rVert$ (for comparison)

$c_vertiii{d}$, $f^vertiii{g}$
end{document}

opnorm{a}        % normal size
opnorm[big]{a}  % slightly larger
opnorm[Bigg]{a} % largest
opnorm*{a}       % left and right

documentclass{article}
usepackage{amsmath,amssymb}
makeatletter
newcommand{opnorm}{@ifstar@opnorms@opnorm}
newcommand{@opnorms}[1]{%
  left|mkern-1.5muleft|mkern-1.5muleft|
   #1
  right|mkern-1.5muright|mkern-1.5muright|
}
newcommand{@opnorm}[2][]{%
  mathopen{#1|mkern-1.5mu#1|mkern-1.5mu#1|}
  #2
  mathclose{#1|mkern-1.5mu#1|mkern-1.5mu#1|}
}
makeatother

begin{document}

$opnorm{a}$,
$opnorm[Big]{int_0^1 a(x),mathrm{d}x}$,
$displaystyle opnorm*{int_0^1 a(x),mathrm{d}x}_{opnorm{a}}$

$lVert a rVert$ (for comparison)

end{document}

documentclass{article}
DeclareFontEncoding{FMS}{}{}
DeclareFontSubstitution{FMS}{futm}{m}{n}
DeclareFontEncoding{FMX}{}{}
DeclareFontSubstitution{FMX}{futm}{m}{n}
DeclareSymbolFont{fouriersymbols}{FMS}{futm}{m}{n}
DeclareSymbolFont{fourierlargesymbols}{FMX}{futm}{m}{n}
DeclareMathDelimiter{VERT}{mathord}{fouriersymbols}{152}{fourierlargesymbols}{147}
begin{document}
The quick brown fox jumps over the lazy dog.
[
VERT x VERT quad leftVERTfrac{1}{2}rightVERT
]
end{document}

documentclass{article}
%usepackage{mathabx}

% Math symbol font matha
DeclareFontFamily{U}{matha}{hyphencharfont45}
DeclareFontShape{U}{matha}{m}{n}{
      <5> <6> <7> <8> <9> <10> gen * matha
      <10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
      }{}
DeclareSymbolFont{matha}{U}{matha}{m}{n}
DeclareFontSubstitution{U}{matha}{m}{n}

% Math symbol font mathb
DeclareFontFamily{U}{mathx}{hyphencharfont45}
DeclareFontShape{U}{mathx}{m}{n}{
      <5> <6> <7> <8> <9> <10>
      <10.95> <12> <14.4> <17.28> <20.74> <24.88>
      mathx10
      }{}
DeclareSymbolFont{mathx}{U}{mathx}{m}{n}
DeclareFontSubstitution{U}{mathx}{m}{n}

% Symbol definition
DeclareMathDelimiter{vvvert}{0}{matha}{"7E}{mathx}{"17}

begin{document}
[
  leftvvvert frac{A}{B}rightvvvert
]
end{document}