Some common fixed points results via the degree of nondensifiability

In this paper, under suitable conditions and by using the so-called degree of nondensifiability (DND), we provide sufficient conditions for the existence of a common fixed point for two commuting self-mappings defined into a non-empty, bounded, closed and convex subset of a Banach space. Our main result generalizes a Darbo-type fixed point theorem based on the DND. To illustrate the differences between our results and a known common fixed point result for two commuting self-mappings due to Jungck or others based on the measures of noncompactness, we provide some examples.

Keywords:

Fixed points , Common fixed points , Darbo fixed point theorem , Degree of Nondensifiability , \alpha-dense curves