A fixed point theorem in partially ordered sets and some applications to matrix equations
نویسندگان
چکیده
منابع مشابه
A Fixed Point Theorem in Partially Ordered Sets and Some Applications to Matrix Equations
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.
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and Applied Analysis 3 Besides, if for any x, y ∈ M, there exists z ∈ M which is comparable to x and y, 2.4 then f has a unique fixed point. Proof. We first show that f has a fixed point. Since x0 f x0 and f is an increasing function, we obtain by induction that x0 f x0 f2 x0 f3 x0 · · · f x0 · · · . 2.5 Put xn 1 f x0 , n 1, 2, . . . For each integer n ≥ 1, from 2.5 , we have xn xn 1, then by 2...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-07220-4