Dotson, W. G. jun. On the Mann iterative process. (English) Zbl 0203.14801 Trans. Am. Math. Soc. 149, 65-73 (1970). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 66 Documents PDF BibTeX XML Cite \textit{W. G. Dotson jun.}, Trans. Am. Math. Soc. 149, 65--73 (1970; Zbl 0203.14801) Full Text: DOI OpenURL References: [1] 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. , https://doi.org/10.1090/S0002-9904-1966-11543-4 F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571 – 575. · Zbl 0138.08201 [2] 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. · Zbl 0161.20103 [3] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. · Zbl 0084.10402 [4] W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217 – 240. · Zbl 0034.06404 [5] M. Edelstein, A remark on a theorem of M. A. Krasnoselski, Amer. Math. Monthly 73 (1966), 509 – 510. · Zbl 0138.39901 [6] M. A. Krasnosel\(^{\prime}\)skiĭ, Two remarks on the method of successive approximations, Uspehi Mat. Nauk (N.S.) 10 (1955), no. 1(63), 123 – 127 (Russian). [7] W. Robert Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506 – 510. · Zbl 0050.11603 [8] S. Mazur, Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält, Studia Math. 2 (1930), 7-9. · JFM 56.0091.01 [9] Zdzisław Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591 – 597. · Zbl 0179.19902 [10] C. L. Outlaw and C. W. Groetsch, Averaging iteration in a Banach space, Notices Amer. Math. Soc. 15 (1968), 180. Abstract #653-342. [11] B. J. Pettis, A proof that every uniformly convex space is reflexive, Duke Math. J. 5 (1939), no. 2, 249 – 253. · Zbl 0021.32601 [12] Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math. Verein. 59 (1957), no. Abt. 1, 131 – 140 (German). · Zbl 0077.11002 [13] J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180. · JFM 56.0355.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.