So if I understand right, you haven't checked MathSciNet? Well, it's not much use:
- Park's paper is http://www.ams.org/mathscinet-getitem?mr=2144066 but there is no review.
- Park's survey paper is http://www.ams.org/mathscinet-getitem?mr=2188170 but there is only a "summary".
- Those are the only things you are lead to by citations.
(Community Wiki so others can edit if they wish; and this is hardly an answer worthy of gain rep for.)
Edit (Sergey Melikhov): As I finally got the chance to get to my office and browse Mathscinet, I am led to something interesting by citations. The 2004 paper of Park, which has no review, is cited in the review of his another paper [Remarks on recent results in analytical fixed point theory. Nonlinear analysis and convex analysis, 517–525, Yokohama Publ., Yokohama, 2007], which says:
Summary: "We show that some fixed point theorems and related results in our previous works [a long list of Park's papers including the 2004 paper] need additional requirements for their validities. Some of the new correct results appear in [S. Park, J. Nonlinear Convex Anal. 7 (2006), no. 1, 1-17]."
The review of the latter paper doesn't explicitly mention the compact AR problem, but it will probably take me a while to get the 2006 and 2007 papers.
