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- W2502257305 abstract "Abstract. The main result of the paper unifies two important fixed point the-orems published in the same year, 1965, the first one discovered independentlyby Browder [F.E. Browder, Nonexpansive nonlinear operators in Banach spaces,Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 1041–1044], G¨ohde [D. G¨ohde, ZumPrinzip 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 toPresi´c [S.B. Presi´c, Sur une classe d’ in´equations aux diff´erences finite et surla convergence de certaines suites, Publ. Inst. Math. (Beograd)(N.S.), 5(19)(1965), 75–78]. In this way we show how amazingly two apparently differentbeautiful results in mathematics can meet after almost half a century!MSC 2000. 47H10, 54H25.Keywords. Banach space, Presi´c type contraction condition, fixed point, k-stepiteration procedure, nonexpansive type operator.1. INTRODUCTION One of the most interesting generalizations of Banach’s contraction mappingprinciple has been obtained in 1965 by S. Presi´c [19]:Theorem 1 (S. Presi´c [19], 1965). Let (X,d) be a complete metric space,k a positive integer, α" @default.
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- W2502257305 date "2009-01-01" @default.
- W2502257305 modified "2023-09-27" @default.
- W2502257305 title "AN ITERATIVE METHOD FOR APPROXIMATING FIXED POINTS" @default.
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