Activist investor Carl Icahn said he bought another half-billion dollars' worth of Apple Inc. stock on Tuesday, his third investment in the iPhone maker in less than a week, which boosts his stake to more than $4 billion.

Icahn, who argues the shares are undervalued, has provided a blow-by-blow on Twitter of every new investment he's made in the company since last Wednesday, when he first disclosed a $500 million purchase that took him to a $3 billion position. He did so again on Thursday.

On Tuesday, he tweeted: "Just bought $500 mln more $AAPL shares."

"My buying seems to be going neck-and-neck with Apple's buyback program, but hope they win that race."

Icahn is waging a public campaign to get Apple to return more cash to shareholders, and has filed a resolution proposing that it gives back $50 billion more through share buybacks.

Apple, on its part, argues it already has one of the industry's largest capital-return programs in place.

It said on Monday it had returned an additional $7.7 billion in cash to shareholders through dividends and share repurchases during the December quarter, bringing cumulative payments to over $43 billion, out of a total plan to dole out $100 billion.

Shares of Apple slumped almost 8 percent to $508 in midday trading, walloped by lower-than-expected iPhone sales and a weak revenue forecast for the March quarter.