Jana Partners' Barry Rosenstein and public pension fund California State Teachers' Retirement System, which together own $2 billion of Apple Inc. (AAPL - Get Report) stock, launched a new kind of activist campaign over the weekend, urging the iPhone maker to take action to curb growing smartphone and iPad addiction among children.

Rosenstein, who typically launches campaigns to drive share price improvement through M&A or operational improvements at target companies, released word of the campaign at the same time he announced that he was starting a new impact investing fund. Rather than pushing for M&A or other changes, the impact investing fund will focus on socially responsible investing.

The combined Jana-CalSTRS stake is miniscule considering Apple's $900 billion market capitalization. However, Rosenstein and CalSTRS' Anne Sheehan hope to make a long-term impact through the fund and investment. The two funds issued a letter Saturday full of statistics and data about child overuse of iPhones and their impact on sleep, depression and risk of suicide.

Giving the activist campaign some gravitas, the campaign includes a high-profile advisory board, including rock star Sting and his wife Trudie Styler. Sister Patricia Daly, a nun who has worked in corporate sustainability and social responsible investing, as well as Robert Eccles, an expert on sustainable strategies, also are on the advisory board.

Rosenstein and Sheehan concluded their letter by seeking to discuss the issue with Apple's board. The duo also urged Apple's board to discuss it with Jana's advisory panel. The two firms also launched a website to promote their campaign, titled "think differently about kids." Rosenstein and Sheehan added that they are not advocating an all-or-nothing approach. They pointed to some research, which suggested that teens could use the devices for one hour or less.

Nevertheless, they recommended that Apple set up a committee of experts including child development specialists to study the issue. In addition, Rosenstein and Sheehan also urged Apple to partner with other experts to research it. They also suggested that Apple could offer new tools and options on the smartphone such as parental monitoring or screen time limiting options. 

The campaign isn't the first insurgency battle Apple has faced. In 2013, billionaire raider-turned-activist Carl Icahn also acquired a $2 billion Apple stake and engaged in a campaign at the smartphone maker. Icahn urged Apple into buying back more stock, which it did. 

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