A Fixed Point Theorem in Partially Ordered Sets and Some Applications to Matrix Equations
نویسندگان
چکیده
An analogue of Banach’s fixed point theorem in partially ordered sets is proved in this paper, and several applications to linear and nonlinear matrix equations are discussed.
منابع مشابه
Some Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations
Let $mathcal{X}$ 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. ...
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