in this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. we discuss also the existence of a solution to a nonlinear random integral equation in banah spaces.

A thin rigid plate is submerged beneath the free surface of deep water. The plate performs small-amplitude oscillations. The problem of calculating the radiated waves can be reduced to solving a hypersingular boundary integral equation. In the special case of a horizontal circular plate, this equation can be reduced further to onedimensional Fredholm integral equations of the second kind. If th...

Recently, Wazwaz has studied the regularization method to one-dimensional linear Fredholm integral equations of first kind [Wazwaz, 2011]. In this work, we develop for and nonlinear two-dimensional Fred-holm kind. Indeed, is used directly. But are transformed linearintegral by a change variable; then, The Regularization-Homotopy Method applied. combination homotopy perturbation method, or short...

In this paper, we propose a different way for solving systems of nonlinear Fredholm integral equations the second kind. We construct our new strategy in two steps, through beginning with linearization phase system by applying Newton method, then pass to discretization some involved operator using Nystr\"{o}m method. The convergence analysis method is proved under necessary conditions. At last, ...

Two methods for computing numerical conformai mappings are compared. The first, due to Symm, uses a Fredholm integral equation of the first kind while the other, due to Lichtenstein, uses a Fredholm integral equation of the second kind. The two methods are tested on ellipses with different ratios of major to minor axes. The method based on the integral equation of the second kind is superior if...

Three-body resonances in atomic systems are calculated as complexenergy solutions of Faddeev-type integral equations. The homogeneous FaddeevMerkuriev integral equations are solved by approximating the potential terms in a Coulomb-Sturmian basis. The Coulomb-Sturmian matrix elements of the three-body Coulomb Green’s operator has been calculated as a contour integral of two-body Coulomb Green’s ...

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

In this work we consider the numerical solution of a radiative transfer equation for modeling the emission of photons in stellar atmospheres. Mathematically, the problem is formulated in terms of a weakly singular Fredholm integral equation defined on a Banach space. Computational approaches to solve the problem are discussed, using direct and iterative strategies that are implemented in open s...

Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation. This volume integral equation, however, in general fails to feature a weakly singular integral operator. Nevertheless, after a suitable periodization, the involved integral operator can be efficiently evaluated on trigonomet...