On common fixed point theorems in symmetric spaces with some weaker conditions

Abstract

We obtain common fixed point theorems for two pairs of occasionally weakly compatible maps on symmetric (semimetric) spaces under some weaker conditions. We show that to prove common fixed point theorems for four mappings in symmetric spaces any additional axiom (W3, W4, C.C., H. E.) is not needed. We give examples to illustrate our results. We also extend our results for finite number of mappings. The results of this paper contain many fixed point theorems on metric spaces and symmetric spaces as special case.