Some remarks on best approximation and fixed points (Q1307648)

The main result in this paper is as follows. Ler \(C\) be a nonempty convex subset of a normed linear space \(X\) and \(f:C\to X\) a continuous map. Let \(g:C\to C\) be a continuous, almost quasiconvex and onto map. Further, if \(C\) has a nonempty compact convex subset \(C_0\) such that the set \(B=\{y\in C:\|gx-fy\|\geq\|gy-fy\|,\forall x\in C_0\}\) is compact, then there is a point \(y_0\in C_0\) such that \(\|gy_0-fy_0\|=\inf\{\|fy_0-x\|:x\in C\}\).