On generalized coupled fixed points with applications to the solvability of coupled systems of nonlinear quadratic integral equations. (English) Zbl 1404.45009
Summary: In this paper, we introduce the notion of generalized coupled fixed points and, as a consequence of Darbo’s fixed point theorem associated to an abstract measure of noncompactness, we present a result about the existence of this class of coupled fixed points in Banach spaces. As an application, we investigate the existence of solutions for a class of coupled systems of nonlinear quadratic integral equations of Volterra type.
MSC:
45G15 | Systems of nonlinear integral equations |
47H10 | Fixed-point theorems |
47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |