Fixed point theorems for Lipschitz type maps. (English) Zbl 1069.54028

Authors’ abstract: The aim of this paper is to obtain common fixed point theorems for generalized Lipschitz pairs of non-compatible maps without using the continuity of the maps involved and completeness of the metric space. Coincidence theorems for generalized Lipschitz type quadruples of maps on an arbitrary (nonempty) set with values in a metric space are also obtained. The remarkable aspect of such maps is that they do not need to be continuous at their common fixed points.


54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems