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 \(\lim_{n\to \infty} f(x_n)= \lim_{n\to \infty} g(x_n)\) but \(\lim_{n\to \infty} d(f(g(x_n)), g(f(x_n)))\) 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.


54H25 Fixed-point and coincidence theorems (topological aspects)
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