SOME EXTENSIONS OF CONTRACTIVE MAPPING THEOREMS

Abstract

Some extensions of Edelstein's, Rhoades's, Krasnoselskii's, Browder's, Frum-Ketkov's fixed point theorems are obtained. The existence of fixed points x = T(x, x) and the convergence of implicit iteration xn = T(xn; xn+1) for these type contractive mappings of two variables were investigated. In some cases we also point out that the implicit iteration converges to the fixed points, while the Picard iteration xn = T(xn-1; xn-1) can not. The paper is a continuation of [1, 2, 3].