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Let $$\psi: [0, \infty) \rightarrow R, \psi: [0, \infty) \rightarrow R, f:[0, \infty) \rightarrow R$$ and $$g:[0, \infty) \rightarrow R$$ be functions such that $$f(0)=g(0)=0$$,
$$\psi:(x)=e^{-x} + x, x \geq 0$$,
$$\psi:(x)=e^{2} - 2x - 2e^{-x} + 2 x \geq 0$$,
$$f(x)= \int_{-x}^{x} (|t| - t^{2})e^{-t^{2}} dt, x > 0$$,
and
$$g(x) = \int_{0}^{x^{2}} \sqrt{t} e^{-t} dt, x > 0.$$
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