Quasi Controlled -Metric Spaces over -Algebras with an Application to Stochastic Integral Equations

Coupled fixed point on ordered cone metric spaces with application in integral equations

Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

An Application of Stochastic Integral Equations to Electrical Networks

In this paper we present an application of the Itô stochastic calculus to the problem of modelling inductor-resistor electrical circuits. The deterministic model of the circuit is replaced by a stochastic model by adding a noise term in the source. We also consider the case when both the source and the resistance are random. The analytic solutions of the resulting stochastic integral equations ...

Contractive Mapping in Generalized, Ordered Metric Spaces with Application in Integral Equations

Quasi-metric Spaces with Measure

The phenomenon of concentration of measure on high dimensional structures is usually stated in terms of a metric space with a Borel measure, also called an mm-space. We extend some of the mm-space concepts to the setting of a quasi-metric space with probability measure (pq-space). Our motivation comes from biological sequence comparison: we show that many common similarity measures on biologica...

A wavelet method for stochastic Volterra integral equations and its application to general stock model

In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...