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

Singh, S. L.; Kumar, Ashish

Riv. Mat. Univ. Parma (7) 3, 25-34 (2004).

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.

Reviewer: S. L. Singh (Rishikesh)

MSC:

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

Keywords:

fixed point; coincidence point; R-weakly commuting maps; compatible maps; non-compatible maps; Lipschitz type maps