Picard operators and applications. (English) Zbl 1031.47035

The author gives a survey of known results concerning Picard operator theory. He shows that some results, previously assumed to be set within metric space, are true also in an \(L\)-space. He gives some examples of applications to operator theory, to functional differential equations and to integral equations.


47H10 Fixed-point theorems
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
34A40 Differential inequalities involving functions of a single real variable
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34K10 Boundary value problems for functional-differential equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
41A10 Approximation by polynomials
45N05 Abstract integral equations, integral equations in abstract spaces