On the existence of common fixed points for a pair of lipschitzian mappings in banach spaces

The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L^p spaces, in Hardy spaces H^p, and in Sobolev spaces H^r,p, for 1<p<+∞ and r≥0. Foundation items: the National Natural Science Foundation of China (19801023); the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, P.R. China Biography: ZENG Lu-chuan (1965-)