Burroughs has always been popular in both Europe and Asia and remains so to this day (which might also explain why the movie did much better in those markets than domestic) from almost as soon as he was first published. I don't think that it would be a terribly great stretch of the imagination to say that Kurosawa would have been familiar with Burroughs' work, and, while the single swordsman prevailing against incredible odds, I do recall a scene in "The Gods Of Mars," first published in 1913, in which Carter defeated a room filled with no less than 50 adversaries. And all that impossible jumping that seems so common in all of the chop sockey movies of the70's and 80's certainly would be something that Carter did fairly often in the Mars books.
Far be it from me to say that Burroughs' influence is QUITE that great, but both Asimov and Moorcock have, on more than one occasion, referred to Edgar Rice Burroughs as the most influential and most copied author of the 20th Century.