Some Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations

Let X be a partially ordered set and d be a generalized metric on X. We obtain some results in coupled and coupled coincidence of g-monotone functions on X, where g is a function from X into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in the unit ball of the Hilbert space. Some applications for linear and nonlinear matrix equations are given.