Vector-valued metrics, fixed points and coupled fixed points for nonlinear operators (Q2510625)

The authors study the existence and Hyers-Ulam stability of fixed points of single-valued and multi-valued contraction-type operators on generalized metric spaces in the sense of \textit{A. I. Perov} [Priblizhen. Metody Reshen. Differ. Uravn. 2, 115--134 (1964; Zbl 0196.34703)]. In the second part of the paper, they work in an ordered metric space and prove the existence and uniqueness of the coupled fixed point for a pair of operators satisfying some contraction and mixed monotonicity conditions. The result is applied to a system of functional-integral equations.