SAN FRANCISCO (AP) ― Yahoo CEO Marissa Mayer is getting some unsolicited advice on how to turn around the long-struggling Internet company, just like some of her predecessors who tangled with investors dissatisfied with management’s performance.

In a letter Friday, activist investor Jeffrey Smith urged Yahoo Inc. to buy another fallen Internet star, AOL Inc. and take steps to reduce the future taxes on the company’s lucrative stake in China’s Alibaba Group. He also chastised Mayer for spending $1.3 billion to acquire an Internet blogging service and more than two dozen other startups during the past two years with little to show in return so far.

To bolster his arguments, Smith says he has built a “significant” stake in Yahoo through Starboard Value LP. The size of the stake wasn’t quantified in the letter and hasn’t yet been divulged in regulatory filings. 

The idea of Yahoo and AOL getting together isn’t a new one. Various analysts and other Internet observers have argued a marriage between the two companies would allow them to cut costs, attract more Web surfers and, most importantly, strengthen their online advertising arsenal to improve their chances of competing against Internet stalwarts Google Inc. and Facebook Inc.

“It makes a lot of sense,” said BGC Financial Partners Colin Gillis.

In a statement, Mayer said she looked forward to discussing Smith’s ideas. “Going forward, we have great confidence in the strength of our business,” Mayer said.

AOL didn’t respond to requests for comment Friday.

The prospect of a change in Yahoo’s recent direction seemed to excite investors. Yahoo’s stock rose $1.71, or 4.4 percent, to close at $40.66. AOL’s stock added $1.58, or 3.7 percent, to finish at $44.55 as investors reacted to a potential buyout bid.

Smith agitated for change at AOL in 2012 after he acquired a 5.3 percent stake in that company and mounted an unsuccessful campaign to win three board seats. He didn’t express any interest in trying to replace anyone on Yahoo’s nine-member board, which includes Mayer.

This is the third time in the past six years that an activist investor has targeted Yahoo for a shake-up. Billionaire Carl Icahn seized three spots on Yahoo’s board in 2008 after attacking the company for spurning a $47.5 billion takeover offer from Microsoft Corp. Hedge-fund manager Daniel Loeb also wound up with three board seats in 2012 after orchestrating the ouster of one of Yahoo’s previous CEOs, Scott Thompson.

Since becoming Yahoo’s CEO in July 2012, Mayer has been buying startups and trendy services such as Tumblr in an effort to appeal to a younger demographic and expand Yahoo’s audience on smartphones and tablets as more people rely on those mobile devices to connect with digital services.

Given that AOL is still closely associated to the days when people relied on dial-up modems to surf the Web, Mayer might view a buyout to be “too backward-looking for Yahoo,” Gillis said.