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Fixed point theorems in ordered Banach algebras and applications. (English) Zbl 0964.47026

The author discusses the solvability of the equation \(Ax\cdot Bx=x\) in Banach algebras with cones and indicates some applications to nonlinear integral equations.

MSC:

47H10 Fixed-point theorems
47J05 Equations involving nonlinear operators (general)
45G10 Other nonlinear integral equations
47N20 Applications of operator theory to differential and integral equations
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
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