How can I check if an image style for an image has been created already?
I couldn't find one in the core files but fortunately it's pretty straightforward to implement:

function image_style_path_exists($style_name, $path) {
  $uri = image_style_path($style_name, $path);
  return file_exists($uri);
}


Assuming you have a file object you would call it like this:

$image_exists = image_style_path_exists('thumbnail', $file-&gt;uri);


If you only need to use it once in the site you could boil it down to:

$image_exists = file_exists(image_style_path('thumbnail', $file-&gt;uri));


but it's usually better to separate this sort of thing out into a function