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Fixed point theorems in partially ordered complete metric spaces. (English) Zbl 1225.54030
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:
54H25 Fixed-point and coincidence theorems (topological aspects)
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47H10 Fixed-point theorems
47J25 Iterative procedures involving nonlinear operators
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