On the Mann iterative process
HTML articles powered by AMS MathViewer
- by W. G. Dotson PDF
- Trans. Amer. Math. Soc. 149 (1970), 65-73 Request permission
References
- F. E. Browder and W. V. Petryshyn, The solution by iteration of linear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 566–570. MR 190744, DOI 10.1090/S0002-9904-1966-11543-4
- J. B. Diaz and F. T. Metcalf, On the structure of the set of subsequential limit points of successive approximations, Bull. Amer. Math. Soc. 73 (1967), 516–519. MR 211387, DOI 10.1090/S0002-9904-1967-11725-7
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217–240. MR 36455, DOI 10.1090/S0002-9947-1949-0036455-9
- M. Edelstein, A remark on a theorem of M. A. Krasnoselski, Amer. Math. Monthly 73 (1966), 509–510. MR 194866, DOI 10.2307/2315474
- M. A. Krasnosel′skiĭ, Two remarks on the method of successive approximations, Uspehi Mat. Nauk (N.S.) 10 (1955), no. 1(63), 123–127 (Russian). MR 0068119
- W. Robert Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510. MR 54846, DOI 10.1090/S0002-9939-1953-0054846-3 S. Mazur, Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält, Studia Math. 2 (1930), 7-9.
- Zdzisław Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591–597. MR 211301, DOI 10.1090/S0002-9904-1967-11761-0 C. L. Outlaw and C. W. Groetsch, Averaging iteration in a Banach space, Notices Amer. Math. Soc. 15 (1968), 180. Abstract #653-342.
- B. J. Pettis, A proof that every uniformly convex space is reflexive, Duke Math. J. 5 (1939), no. 2, 249–253. MR 1546121, DOI 10.1215/S0012-7094-39-00522-3
- Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math.-Verein. 59 (1957), no. Abt. 1, 131–140 (German). MR 84116 J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180.
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 149 (1970), 65-73
- MSC: Primary 47.80; Secondary 65.00
- DOI: https://doi.org/10.1090/S0002-9947-1970-0257828-6
- MathSciNet review: 0257828