Document Type : Original Article

Author

• Gonzalo Garcia

Universidad Nacional de Educacin a Distancia (UNED), Departamento de Matemaicas. 03202 Elche (Alicante), Spain

Abstract

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