Global convergence of successive approximations of solutions for functional differential equations with infinite delay
The author consideres the initial value problem for functional differential equations with infinite delay (IP): \(dx/dt=f(t,x_ t),\) \(t\geq \sigma\), \(x_{\sigma}=\phi \in B\), where f is an E-valued mapping defined on \(J\times B\), E is a Banach space with norm \(| \cdot |_ E\), \(J=[\sigma,\sigma +a)\), \(0<a\leq \infty\), B is an abstract phase space with seminorm, or quasinorm \(| \cdot |_ B\) satisfying suitable axioms. In four theorems he proves sufficient conditions for the global convergence of successive approximations for (IP). On the end, the obtained results in this paper are illustrated in two examples.
global convergence of successive approximations
scientific article; zbMATH DE number 4061719