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 generalizedmetric 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.