Two large shareholders have urged Apple to study whether iPhones are proving addictive for children and if intensive use of the smartphones may be bad for their mental health.

The "growing societal unease" over the intensive use of smartphones by children "at some point is likely to impact even Apple," they warned.

"There is a growing body of evidence that, for at least some of the most frequent young users, this may be having unintentional negative consequences" on their health, said Jana Partners LLC and California State Teachers' Retirement System (Calstrs) in a letter sent to Apple last week.

The two shareholders between them own about $2 billion in Apple shares.

They urged the company to develop additional means for parents to restrict the use of mobile phones by their children.

"We specifically ask that Apple form a committee of experts and specialists to research and study this issue and monitor ongoing developments in technology," the letter said.

"Additionally, we encourage Apple to offer parents more tools by enhancing mobile device software to enable age-appropriate setup options including limiting screen time, setting up parental monitoring, etc."

The investors said confronting this issue now would enhance the value of the firm in the long term for all shareholders.

Apple has not commented on the letter, but it provides parental controls on iPhones that allow restricting access to certain apps and content.

Although Apple was singled out in the letter, the question of technology and screen time for children has long been debated.

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