An iterative method for approximating fixed points of Presić nonexpansive mappings - Berinde, Vasile; Păcurar, Mădălina (Rev. Anal. Numér. Théor. Approx., 2009)
Some fixed point theorems of Presić type for nonexpansive mappings\(f: X^k→ X\), where \(k≥ 1\) is an integer, are obtained.The main result of the paper unifies two important fixed point theorems published in the same year, 1965, the first one discovered independently by Browder [F.E. Browder, Nonexpansive nonlinear operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 1041-1044], Göhde [D. Göhde, Zum Prinzip der kontraktiven Abbildung, Math. Nachr., 30(1965), 251-258] and Kirk [W.A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly,72 (1965), 1004-1006], while the second one is due to Presić [S.B. Presić, Sur une classe d’ inéquationsaux differences finite et sur la convergence de certaines suites, Publ. Inst. Math. (Beograd)(N.S.), 5(19) (1965),75-78]. In this way we show how amazingly two apparently different beautiful results in mathematics can meet after almost half a century! This appears to be the first attempt to study multi-step iterative methods by means of the fixed point theory of nonexpansive mappings. Several related results in literature are extended, unified and generalized.