Existence and approximation of solutions of some first order iterative differential equations. (English) Zbl 1224.34014

Berinde, Vasile

Miskolc Math. Notes 11, No. 1, 13-26 (2010).

Summary: Existence theorems for some iterative differential equations as well as convergence theorems for an iterative method designed to approximate these solutions, are proved. To this end, we basically employ the technique of non-expansive mappings.

MSC:

34A45	Theoretical approximation of solutions to ordinary differential equations
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

iterative differential equation; solution; non-expansive operator; fixed point; convergence theorem