File: Investor Carl Icahn (CHIP EAST/REUTERS)

Apple shares climbed more than 5 percent at one point in afternoon trading, following two tweets from billionaire investor Carl Icahn, who said that his firm has a “large position” in the technology company.

Shares of Apple have fallen more than 30 percent from a September high of $705.05, with many investors questioning whether the company can maintain the innovation pace set by its late co-founder Steve Jobs. On Tuesday morning, for example, Oracle chief executive Larry Ellison said that he thinks Jobs is “irreplaceable” and predicted Apple would have a rough time staying ahead of the curve without him.

But Icahn clearly has other thoughts about the technology firm, saying in a Twitter message that he thinks Apple’s stock is “undervalued.”

The noted investor is a relative newcomer to Twitter, having joined in June. Thus far, his feed has been a place for him to share media appearances and crack the occasional joke about his lawsuit to stop a buyout vote at Dell. But on Monday, Icahn Enterprises issued a press release saying that Icahn will use his Twitter account to “communicate with the public about our company and other issues.”

Icahn appears to have opened that line of communication with a bang, saying not only that his firm has a position in Apple, but also that he had met with its chief executive, Tim Cook, to discuss issues such as the firm’s buyback plan.

“Had a nice conversation with Tim Cook today,” Icahn tweeted Monday. “Discussed my opinion that a larger buyback should be done now. We plan to speak again shortly.”

Apple shares, which opened at $470.94 each, saw a boost after Icahn’s remarks and were priced at $493.68 apiece in afternoon trading.

The Securities and Exchange Commission in April clarified rules regarding company disclosures to say that companies could use social media accounts to provide information about their business plans, as long as the firms gave investors proper notice that company news may flow from social networks.

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