On the existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces. (Q1418287)

The author presents several existence theorems for common fixed points of a pair of Lipschitz mappings in \(p\)-uniformly convex Banach spaces. These results were inspired by a fixed point theorem of Krüppel for an asymptotically regular mapping, a common fixed point theorem of Sharma and Thakur for a pair of asymptotically regular mappings, and a fixed point theorem of Lim and Xu for a uniformly \(k\)-Lipschitz mapping. These results are used to establish some common fixed point theorems for a pair of Lipschitz mappings in more particular spaces, such as Hilbert spaces, \(L^p\)-spaces, Hardy spaces \(H^p\), and Sobolev spaces \(H^{r,p}\), for \(1<p<+\infty\) and \(r\geq 0\).