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Zbl 1225.54030
Zhilong, Li
Fixed point theorems in partially ordered complete metric spaces. (English)
[J] Math. Comput. Modelling 54, No. 1-2, 69-72 (2011). ISSN 0895-7177

Summary: We present some fixed point theorems in a partially ordered complete metric space $X$. The usual Caristi's condition that $x\preceq Tx$ for each $x\in X$ is weakened at the expense that the mapping is nondecreasing with respect to a partial order.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
65J15 Equations with nonlinear operators (numerical methods)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47J25 Methods for solving nonlinear operator equations (general)

Keywords: nondecreasing mapping; fixed point; partially ordered complete metric space; bounded from below

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Zentralblatt MATH Berlin [Germany]