Activist investor Carl Icahn’s $1 billion stake in Apple Inc. is getting him dinner with the iPhone maker’s Chief Executive Officer Tim Cook.

Icahn, who has amassed holdings in other technology companies including Yahoo! Inc. and Dell Inc. to agitate for change, is pushing Apple to return more cash to investors than the $100 billion Cook has already committed in dividends and buybacks through 2015. While Icahn’s stake amounts to a small fraction of Apple’s $457 billion market value, he’s still deploying posts on Twitter Inc. to pressure Cook to meet his demands.

“Spoke to Tim,” Icahn wrote on Twitter Thursday. “Planning dinner in September. Tim believes in buyback and is doing one. What will be discussed is magnitude.”

Cook has also faced calls to dole out more money to shareholders from hedge-fund manager David Einhorn of Greenlight Capital LLC. Apple in April unveiled what it called the largest share-repurchase program in corporate history after Einhorn urged the company to return more of its cash.

“Tim Cook is a little bit of an unknown quantity in these activist-investor games,” said Erik Gordon, a business professor at the University of Michigan. “Steve Jobs was a known quantity – he wouldn’t even pick up the phone.”

Steve Dowling, a spokesman for Apple, and Icahn didn’t respond to requests for comment.

Apple, based in Cupertino, California, has faced investor concern about slowing growth. Profit fell 22 percent last quarter and 18 percent in the three-month period before that. The stock was down 5.6 percent this year through Wednesday, compared to a 15 percent gain for Stardard & Poor’s 500 Index.

Product Updates

Icahn is investing in Apple ahead of a batch of product updates. Apple will unveil a new iPhone at a Sept. 10 event, followed by the introduction of new iPads later in the year, people familiar with the plans have said. The anticipation has helped push the stock up 11 percent since June.

Icahn projects Apple’s stock can rise to more than $625 if it buys back shares, a person familiar with his thinking said earlier this month. Icahn wants Apple to borrow $150 billion at a 3 percent interest rate to fund the purchases and avoid paying more taxes, the person added.

Apple’s shares rose less than 1 percent to $502.96 at the close in New York, leaving them down 5.5 percent so far this year.