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Common fixed points of two partially commuting tangential selfmaps on a metric space. (English) Zbl 0977.54037
Two selfmaps f and g of a metric space (X,d) are said to be noncompatible if there exists some sequence {x n } such that lim n f(x n )=lim n g(x n ) but lim n d(f(g(x n )),g(f(x n ))) is either nonzero or nonexistent. In this paper the authors prove two common fixed point theorems for a pair of selfmaps on a metric space without using the full force of noncompatibility and relaxing the Lipschitz type condition.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces