The test problem class of Volterra functional differential equations in Banach space

In this paper, we introduce the test problem classes, which are entitled D-lambda*(alpha, beta, mu(1), mu(2)) and D-lambda*,D-delta(alpha, beta, mu(1), mu(2)) respectively, with respect to the initial value problems of nonlinear Volterra functional differential equations in Banach spaces. A series of stability results of the analytic solution are obtained and a condition estimate for the class D-0(alpha, beta, mu(1), mu(2)) which based on logarithmic matrix norm is also obtained. The above results extend the existing results for ordinary differential equations. (c) 2005 Elsevier Inc. All rights reserved.