Significant market share is enough for antitrust to be a concern. You don't need a monopoly, and indeed most companies engaging in anti-competitive behavior don't.
An example of an antitrust case for someone with market share similar to Apple's in phones would be helpful. To head you off at one unproductive pass: it is unlawful to collude with other companies to fix prices even if you have a minority market share.
Note though that it is an open question whether the relevant market is "phones" or "smartphones".
That's true, but obviously Apple doesn't have a monopoly in either market (obviously, they are dwarfed by the total phone market).
Apple doesn't have anything close to a significant market share.
There is LOTS of competition in the market place.
Apple has significant market share. They just don't have anything close to a monopoly.