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

In this paper, we introduce the test problem classes, which are entitled Dλ∗(α,β,μ1,μ2) and Dλ∗,δ(α,β,μ1,μ2) 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 D0(α, β, μ1, μ2) which based on logarithmic matrix norm is also obtained. The above results extend the existing results for ordinary differential equations.