Do we have this symbol in mathematics? 
It is the symbol I used to show left hand side of inequality isn't greater than right hand side.
More precisely I used this to show the below matrix is not diagonally dominant:
$$\begin{bmatrix}5&6&7\\
2&-4&2\\
3&2&-5\\
\end{bmatrix}$$
So at the first row I want to emphasize that $|5|$ is not greater than $|6|+|7|$  therefor instead of writing $|5|<|6|+|7|$ I used the symbol in the image above.
Is it ok to use this symbol in mathematics?

I would also say that we have both relations
$$
x \not\le y, \quad x\not \ge y.
$$
There are variants, of course, like
$$
x \lneq y,\quad x \gneq y 
$$
and
$$
x\nless y, x\ngtr  y
$$
