An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations. (English) Zbl 1466.47040

Samadi, A.; Ghaemi, M.

Filomat 28, No. 4, 879-886 (2014).

Summary: In this paper, an extension of G. Darbo’s fixed point theorem [Rend. Semin. Mat. Univ. Padova 24, 84–92 (1955; Zbl 0064.35704)] is introduced. By applying our extension, we obtain a coupled fixed point theorem and a solution for an integral equation. The proofs of our results are based on the technique of measure of noncompactness.

MSC:

47H10	Fixed-point theorems
47H08	Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
47N20	Applications of operator theory to differential and integral equations

Keywords:

measure of noncompactness; Darbo fixed point theorem; Schauder fixed point theorem; coupled fixed point; integral equation

Citations:

Zbl 0064.35704