Activist investor Carl Icahn turned up the pressure on Apple Inc. on Thursday by announcing that he'd bought an additional $500 million worth of stock in the company. Icahn also filed an official letter outlining the reasons he believes Apple should increase its stock buyback if shareholders approve an advisory ballot measure next month at the company's annual meeting. "Bought another $500mil of $AAPL tday, bringing our total to $3.6 billion," Icahn tweeted. "If board doesn't see AAPL's 'no brainer' value we sure do." The latest update comes just a day after Icahn revealed he had acquired $500 million in Apple stock in recent months. Icahn says he has now bought $1 billion in stock in the past two weeks. In a letter to Apple shareholders, he explained his rationale for his buyback campaign. "Over the course of my long career as an investor and as chairman of Icahn Enterprises, our best-performing investments result from opportunities that we like to call 'no brainers,' " he wrote.