What type of appositive is your brother mike is getting to be a big boy?

In the sentence "Your brother Mike is getting to be a big boy," "Mike" is a non-restrictive appositive. It provides additional information about "your brother" but is not essential to the meaning of the sentence; the sentence would still make sense without it. Non-restrictive appositives are typically set off by commas, but in this case, the lack of commas makes it a bit ambiguous, suggesting that "Mike" is a specific identification rather than an additional description.