A SECOND ORDER ALGORITHM FOR SYSTEM OF FUNCTIONAL EQUATIONS

Abstract

In this paper, we give a condition for the quadratic convergence of the following system of functional equations f_i (x)=∑_(j=1)^n▒∑_(k=1)^m▒〖a_ijk [x,f_j (S_ijk (x))]+g_i (x),i= ,x ∈_i,i=1,…,n,〗 where _i  Rp are compact or noncompact domains, the given functions g_i: _i → R, S_ijk : _i → _j, aijk: _i x R → R ,1  i, j  n, 1  k  m, are continuous and fi: _i → R are unknown functions.