On the generalized successive approximations method

Abstract

In this paper, denoted a continuous function from [0,1]2 into [0,1] by f, we consider the iterative process: $$f(y,x) = x \ne y = f(x,y),$$ , and we dealt with the question of global convergence of above iterative process, i.e. the question of convergence, for each point(x1,x0) of [0,1]2, of sequence ℕ of points of [0,1] obtained from (I).