Carl Icahn, the billionaire investor, has increased his Apple, Inc stake to over $3 billion. He added to one of his largest holdings while continuing to push the maker of iPads and iPhones to buy back stock.

Icahn announced he had purchased another $500 million of Apple stock over the last two weeks. He called the new the purchase a no brainer and said a letter would be coming soon urging the company to repurchase additional shares.

Icahn announced that there was nothing he found wrong with Apple’s management, but he believes the board is wrong for not taking advantage of the undervalued situation Apple has in not using the capital it has.

Icahn, with his $3 billion stake, owns less than 1% of the company based in Cupertino, California. Icahn, who is 77, first disclosed he had an Apple stake in August of 2013, when the stock was worth $468 per share.

Since then the stock has increased in value by 19%. Icahn, who has earned billions by purchasing stakes in businesses and then pushing them publicly for changes to increase the value of the stock, has been pushing Apple to return some of its cash to its shareholders over the last five months.

Prior to the involvement of Icahn in Apple, its CEO Tim Cook announced a company plan for $100 billion in buybacks and dividends.

Icahn wrote in Wednesday’s tweets that the board at Apple was doing a disservice to its shareholders by not increasing it buyback.

Apple was up 1% on Wednesday to close at $551.51. The stock is up 9.3% over the last year, trailing the 24% advance by the S&P 500 index.

As of the end of September 2013, Icahn Associates had a stake of 3.88 million shares of Apple, which were worth $1.85 billion, the fourth largest holding the company had.

Apple has recommended that investors vote against the proposal by Icahn for a committed buy back of no less than $50 billion in shares during fiscal 2014.

Apple said it its proxy that it was considering options for the return of additional cash to its shareholders, while it also evaluated where to make additional investments with its capital.