Dr. El Sayed Ahmed Mohamed Ghorayeb :: Publications:

In this paper we propose an approximate method for finding approximate solution of mixed additive nonlinear Volterra-Fredholm integral equations in the space (p ~ 1). Using the linear polynomial operators, we replace the given equation by nonlinear inter,ral equation of Hammerstein type with degenerate kernel, and taking the solution of it as an approximate solution to the given equation. It is well known that [1-3], the linear polynomial operator Un(g;x) is a good approximation to the 2n-periodic function g(x) in the space L [O,2n). p If g(x) has the Fourier coefficients a. ,b., then '" 1 1 g(x) ~ iao + i~l [aicos ix + b i cos ixJ; (1)