1. Let us recall the basic definitions of the theory of Orlicz spaces (see, for example, [1]). Henceforth (Ω,A, μ) is the triple consisting of a set Ω, σ-algebra A of its subsets and a σ-additive measure μ defined on A. It is assumed that μ is continuous on Ω (that is any set of positive measure can be divided into two sets of equal measures) and is finite: μ(Ω) < ∞. Let M : [0,+∞) → [0,+∞) be ...

In this paper a numerical method for finding the solution of FredholmHammerstein integral equations is proposed. At first the properties of the Walsh-hybrid functions, which combination of block-pulse functions and Walsh functions are proposed. The properties of the hybrid functions with the operational matrix of integration together Newton-Cotes nodes are then utilized to reduce the solution o...

System identification is very important to technical and nontechnical areas. All physical systems are nonlinear to some extent and it is natural better to use nonlinear model to describe a real system. The Wiener and Hammerstein systems are proved to be good descriptions of nonlinear dynamic systems in which the nonlinear static subsystems and linear dynamic subsystems are separated in differen...

Nyström method is a standard numerical technique to solve Fredholm integral equations of the second kind where integration kernel approximated using quadrature formula. Traditionally, rule used classical polynomial Gauss quadrature. Motivated by observation that given function can be better spline lower degree than single piece higher degree, in this work, we investigate use Gaussian rules for ...