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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.

##### 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