Résumé: This paper focuses on the problem of h-stability of certain classes of dynamic perturbed systems on time scales using time scale versions of some Grönwall type inequalities.We prove under certain conditions on the nonlinear perturbations that the resulting perturbed nonlinear initial value problem still acquire h-stable, if the associated abstract dynamic equation has already owned this property. The paper ends up with two illustrative examples to highlight the utility of our results.

Résumé: In this paper, we consider a variant of projected Tikhonov regularization method for solving Fredholm integral equations of the first kind. We give a theoretical analysis of this method in the Hilbert space L2(a, b) setting and establish some convergence rates under certain regularity assumption on the exact solution and the kernel k(·, ·). Some numerical results are also presented.