Discrete continuation method for nonlinear integral equations in Banach spaces (Q2755034)

In a recent paper [J. Comput. Appl. Math. 113, No. 1-2, 267-281 (2000; Zbl 0939.34021)] the author developed a method to extend Granas Continuation Principle for contractive mappings on complete metric spaces to spaces endowed with two metrics and completed by an iterative approximation procedure. In the present paper, he has used that method to show the existence of unique solution of Urysohn integral equation of the form \(u(t)=\int_0^t f(t,s,u(s))ds\), \(t\) belongs to closed interval of \([0,T]\) in a Banach space, where the integral is understood in the sense of Bochner.