Abstract
In Lakshmikantam et al., J. Nonlinear Analysis Appl. (to appear), Lakshmikantam and Vatsala, J. Inequalities Appl. (to appear) and Shaw and Yakur (to appear), the investigation of the initial value problems of differential equations relative to the changes in the initial time is initiated and an approach is discussed. In this paper, another direction is taken to study the same situation obtaining different set of conditions.