documentclass{article}
usepackage{amsmath,amsthm}

theoremstyle{definition}
newtheorem{examplex}{Example}
newenvironment{example}
  {pushQED{qed}renewcommand{qedsymbol}{$triangle$}examplex}
  {popQEDendexamplex}

begin{document}

begin{example}
This has only text.
end{example}

begin{example}
This has also a display at the end:
begin{align*}
f(x) &= bigg( g(x) bigg) \
h(x) &= bigg( r(x) bigg).qedhere
end{align*}
end{example}

end{document}