On Quadratic Integral Equations of Urysohn Type in Fréchet Spaces
نویسندگان
چکیده
0 u(t, s, x(s)) ds, t ∈ J := [0,+∞), where f : J → R, u : J × [0, T ] × R → R are given functions and A : C(J,R) → C(J,R) is an appropriate operator. Here C(J,R) denotes the space of continuous functions x : J → R. Integral equations arise naturally from many applications in describing numerous real world problems, see, for instance, books by Agarwal et al. [1], Agarwal and O’Regan [2], Corduneanu [8], Deimling [13], O’Regan and Meehan [18] and the references therein. On the other hand, also quadratic integral equations have many useful applications in describing numerous events and
منابع مشابه
A numerical solution of mixed Volterra Fredholm integral equations of Urysohn type on non-rectangular regions using meshless methods
In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it ...
متن کاملFixed Point Theory in Fréchet Spaces for Mönch Inward and Contractive Urysohn Type Operators
We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss Mönch Kakutani and contractive type maps.
متن کاملSome extensions of Darbo's theorem and solutions of integral equations of Hammerstein type
In this brief note, using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove an existence result for a quadratic integral equation of Hammerstein type on an unbounded interval in two variables which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the effic...
متن کاملOn the numerical solution of Urysohn integral equation using Legendre approximation
Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...
متن کاملProducts of Fréchet Spaces
We give a survey of results and concepts related to certain problems on the Fréchet-Urysohn property in products. This material was presented in a workshop at the 2005 Summer Conference on Topology and its Applications at Denison University.
متن کامل