The convergence of a new iteration process for the solution of nonlinear functional equations in banach space

A new iteration process is used to prove several theorems concerning the existence of solutions of the functional equation F(x)=0 where F(x) is a nonlinear functional in Banach space. An advantage of the process under consideration over analogous process using tangential parabolas and tangential hyperbolas, which have rates of convergence of the same order, is the fact that in it second-order Frechet derivatives do not have to be calculated.Translated from Matematicheskie Zametki, Vol. 4, No. 3, pp. 313–322, September, 1968.