Android requires 5 different resolution of images and ios requires 3 different resolution of images during development.
Does unity requires different resolutions of images while building for android or ios?
The short answer is NO. But it's way more complicated than that.
On unity, you can always submit your icon once and it will resize to each required size on each platform you'd like to publish your app. You can see that on player settings. Build Settings > Player Settings > Icon. You can also submit your own custom icon for each platform selecting the checkbox "Override for ...", there you can submit different sizes for each platform.
Now comes the tricky part. During the last four years, I've published 7 games and I ALWAYS had problems with icons on iOS and XCode. When publishing your game to iOS, I never tested the cloud build but whenever you build your game to iOS locally, you'll be prompt with a Xcode file that you have to edit before building for profiling and archiving which will allow you to publish your game to iTunes Connect. This is the part where I constantly have problems. I didn't test the new 2017 version but before that, some required icon sizes were not filled correctly so you had to go and drag from your computer. It's better to be ready to, MAYBE, fill some icon sizes yourself.
Another thing you might notice is that on store listing, you might have problems with icon sizes too. For example: For your google play listing, you'll require a 512x512 icon. For your iTunes Connect, you'll require a 1024x1024 icon and for Windows Phone, much like apple, you'll require all sorts of icon sizes. The same goes for screenshots.
But TL:DR: For Unity, you can always submit your icon once and Unity will resize it for each platform and required size you need. You can check that under Build Settings > Player Settings > Icon