In this paper, we develop a technique for obtaining the rate of convergence attractors dissipative Morse-Smale semiflow under standard and singular perturbations. We have that our is optimal in sense that, it coincides with resolvent operators quasi-linear equations. As applications, improve second-order equation considered [9].

Abstract We consider the harmonic heat flow for maps from a compact Riemannian manifold into that is complete and of non-positive curvature. prove if converges to limiting map non-degenerate critical point energy functional, then rate convergence exponential (in $$L^2$$ L 2 </mml:m...

Under the assumption that the true density is decreasing, it is well known that the Grenander estimator converges at rate n−1/3 if the true density is curved (Prakasa Rao, 1969) and at rate n−1/2 if the density is flat (Groeneboom and Pyke, 1983; Carolan and Dykstra, 1999). In the case that the true density is misspecified, the results of Patilea (2001) tell us that the global convergence rate ...