in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....

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...

In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary and conditions. Some properties of eigenvalues eigenfunctions are investigated. Asymtotic representation eigenfunction obtained. Reconstruction the shown by Weyl function.

We apply the discrete version of Calderón’s reproducing formula and Littlewood–Paley theory with weights to establish the H w → H w (0 < p < ∞) and H w → Lw (0 < p ≤ 1) boundedness for singular integral operators and derive some explicit bounds for the operator norms of singular integrals acting on these weighted Hardy spaces when we only assume w ∈ A∞. The bounds will be expressed in terms of ...

We develop a function theory associated with Dirac type operators on Lipschitz subdomains of Riemannian manifolds. The main emphasis is on Hardy spaces and boundary value problems, and our aim is to identify the geometric and analytic assumptions guaranteeing the validity of basic results from complex function theory in this general setting. For example, we study PlemeljCalderón-Seeley-Bojarski...

Let Ω ⊂ Ω̃ be open sets in R, I ⊂ R be an open neighborhood of the origin and let η be a compactly supported smooth function on Ω× I; we assume that η(·, 0) does not vanish identically. For each x ∈ Ω let t 7→ Γ(x, t) ⊂ Ω̃ be a regular parametrization of a submanifold Mx ⊂ Ω̃ with codimension l. We assume that Γ(x, t) ⊂ Ω if (x, t) ∈ supp η, and that Γ satisfies Γ(x, 0) = x and depends smoothly on...

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of the domain, ...