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

Abstract In this paper, we introduce the test problem classes, which are entitled D λ ∗ ( α , β , μ 1 , μ 2 ) and D λ ∗ , δ ( α , β , μ 1 , μ 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 ( α ,  β ,  μ 1 ,  μ 2 ) which based on logarithmic matrix norm is also obtained. The above results extend the existing results for ordinary differential equations.

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