Picard operators and applications. (English) Zbl 1031.47035

Rus, Ioan A.

Sci. Math. Jpn. 58, No. 1, 191-219 (2003).

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.

Reviewer: Klaudiusz Wojcik (Kraków)

MSC:

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

Keywords:

Picard operators; fixed points; \(L\)-space