It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T ),Ω = {(x,y) : √ x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T ]. Also in...

The aim of the paper is to provide some regularity results for stochastic convolutions corresponding to stochastic Volterra equations in separable Hilbert space. We study convolutions of the form WΨ(t) := ∫ t 0 S(t − τ)Ψ(τ)dW (τ), t ≥ 0, where S(t), t ≥ 0, is so-called resolvent for Volterra equation considered,Ψ is an appropriate process and W is a cylindrical Wiener process. In the paper we e...

Generalized matrix Lotka-Volterra lattice equations are obtained in a systematic way from a “master equation” possessing a bicomplex formulation.

We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck's ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed rst-kind Volterra equation is seen to be the limit of a sequence of solutions of well...

A novel coordinate transformation is used to reduce a simple generalization of the Lotka-Volterra dynamical system to a single second-order autonomous ordinary differential equation. Formal analytic solutions to this differential equation are presented which are shown to reduce to the recently obtained solution to the LotkaVolterra system [C. M. Evans and G. L. Findley, J. Math. Chem. 25 (1999)...

The adaptation of Volterra lters by one particular method, the method of least mean squares (LMS), while easily implemented, is complicated by the fact that upper bounds for the values of step sizes employed by a parallel update LMS scheme are diicult to obtain. In this paper, we propose a modiication of the Volterra lter in which the lter weights of a given order are optimized independently of...