We derive moment inequalities for the supremum of empirical processes of U-Statistic structure and give application to kernel type density  estimation ‎and estimation of the distribution function for functions of observations.  

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...