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

Dhage, B. C.

Panam. Math. J. 9, No. 4, 83-102 (1999).

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.

Reviewer: Jürgen Appell (Würzburg)

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

Keywords:

Banach algebras with cones; nonlinear integral equations