Is there a mathematical operator symbol to express that the left side of the operator is within $\delta$ of the right side? For example: $$y - \delta \leqslant x \leqslant y + \delta$$ could be expressed using this operator I'm looking for: $$x \text{ near}_\delta\text{ } y$$ where $\text{near}_\delta$ is the operator I hope to find. If an operator for this doesn't exist, what would be an appropriate operator to define for this purpose?
I'm looking specifically for operator notation because ultimately I need to have cases: $$x \text{ near}_\delta\text{ } \begin{cases}0&\text{if }w<0,\\y^2&\text{if }0 \leqslant w \leqslant 2,\\-y + \log_z y&\text{if }w>2.\end{cases}$$