in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

The following limit result holds for the weak–type (1,1) constant of dilation-commuting singular integral operator T in Rn: for f ∈ L1(Rn), f ≥ 0, lim λ→0 λ m{x ∈ R : |Tf(x)| > λ} = 1 n ∫ Sn−1 |Ω(x)|dσ(x)‖f‖1. For the maximal operator M , the corresponding result is lim λ→0 λ m{x ∈ R : |Mf(x)| > λ} = ‖f‖1.

Some existence and uniqueness theorems are established for weakly singular Volterra and Fredholm-Volterra integral equations in C[a, b]. Our method is based on fixed point theorems which are applied to the iterated operator and we apply the fiber Picard operator theorem to establish differentiability with respect to parameter. This method can be applied only for linear equations because otherwi...

By constructing an available integral operator and combining fixed point index theory with properties of Green’s function, this paper shows the existence of multiple positive solutions for a class of impulsive singular boundary value problems with integral boundary conditions. Our results extend some recent work in the literature on boundary value problems of ordinary differential equations. We...

Abstract. In this paper wavelet packet bases are used for an estimation of the autoregressive Hilbertian processes operator. We assume that integral operator kernel can have some singular structures and estimate them by projecting functional processes on suitable bases. Linear methods for continuous-time prediction using Hilbert-valued autoregressive processes are compared with the suggested me...