0 |f(s)|ds ≤ |t| ≤ 1. Therefore the image of Bp is (uniformly) bounded. By Arzela-Ascoli, V : L p[0, 1]→ C[0, 1] is compact. The preceeding argument does not go through when V acts on L1[0, 1]. In this case equicontinuity fails, as is demonstrated by the following family {fn} ⊂ B1: fn(s) = n1[0,1/n](s). This suffices to preclude compactness of V ; in particular, V fn has no Cauchy subsequence. ...

In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In addition, it is described its extreme points. Besides, we study certain limit behaviors of such operators and give some more examples of Volterra operators ...

The response of visual cells is a nonlinear function of their stimuli. In addition, an increasing amount of evidence shows that visual cells are optimized to process natural images. Hence, finding good nonlinear models to characterize visual cells using natural stimuli is important. The Volterra model is an appealing nonlinear model for visual cells. However, their large number of parameters an...

A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is test...

in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.

In the paper stochastic Volterra equations of nonscalar type in Hilbert space are studied. The aim of the paper is to provide some results on stochastic convolution and mild solutions to those Volterra equations. The motivation of the paper comes from a model of aging viscoelastic materials. The pseudo-resolvent approach is used.

In this note we give a generalization of a mean value problem which can be viewed as a problem related to Volterra operators. This problem can be seen as a generalization of a result concerning the zeroes of a Volterra operator in the Banach space of continuous functions with null integral on a compact interval.

Absfrucf -Volterra filters are a particular class of nonlinear filters defined by an extension of the concept of impulse response to the nonlinear case. Linear-quadratic filters are a special example of Volterra filters limited to the second order. In the first part of this paper it is shown that all the results recently published, valid in the linear-quadratic case, can be extended with the ap...