University of MaraghehSahand Communications in Mathematical Analysis2322-580717220200601Some Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations37533741010.22130/scma.2018.86797.440ENHasanHosseinzadehDepartment of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.0000-0002-1723-4140Journal Article20180524Let $\mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $\mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $\mathcal{X}$, where $g$ is a function from $\mathcal{X}$ 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.https://scma.maragheh.ac.ir/article_37410_66eea9cbee3a9a5ccfbce5ff9cbcd2b5.pdf