• [1] 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. MR 0190745 (32 #8155b), http://dx.doi.org/10.1090/S0002-9904-1966-11544-6
• [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. MR 0211387 (35 #2268), http://dx.doi.org/10.1090/S0002-9904-1967-11725-7
• [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, 1958. MR 0117523 (22 #8302)
• [4] W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217–240. MR 0036455 (12,112a), http://dx.doi.org/10.1090/S0002-9947-1949-0036455-9
• [5] M. Edelstein, A remark on a theorem of M. A. Krasnoselski, Amer. Math. Monthly 73 (1966), 509–510. MR 0194866 (33 #3072)
• [6] 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 (16,833a)
• [7] W. Robert Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510. MR 0054846 (14,988f), http://dx.doi.org/10.1090/S0002-9939-1953-0054846-3
• [8] S. Mazur, Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält, Studia Math. 2 (1930), 7-9.
• [9] Zdzisław Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591–597. MR 0211301 (35 #2183), http://dx.doi.org/10.1090/S0002-9904-1967-11761-0
• [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. MR 1546121, http://dx.doi.org/10.1215/S0012-7094-39-00522-3
• [12] Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math. Verein. 59 (1957), no. Abt. 1, 131–140 (German). MR 0084116 (18,811g)
• [13] J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180.

Bibliography

[1]

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. MR 32 #8155b. MR 0190745 (32:8155b)

[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. MR 35 #2268. MR 0211387 (35:2268)

[3]

N. Dunford and J. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)

[4]

W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217-240. MR 12, 112. MR 0036455 (12:112a)

[5]

M. Edelstein, A remark on a theorem of M. A. Krasnoselski, Amer. Math. Monthly 73 (1966), 509-510. MR 33 #3072. MR 0194866 (33:3072)

[6]

M. A. Krasnosel'skiĭ, Two remarks on the method of successive approximations, Uspehi Mat. Nauk 10 (1955), no. 1 (63), 123-127. (Russian) MR 16, 833. MR 0068119 (16:833a)

[7]

W. Robert Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510. MR 14, 988. MR 0054846 (14:988f)

[8]

S. Mazur, Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält, Studia Math. 2 (1930), 7-9.

[9]

Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. MR 35 #2183. MR 0211301 (35:2183)

[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), 249-253. MR 1546121

[12]

H. Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math.-Verein. 59 (1957), 131-140. MR 18, 811. MR 0084116 (18:811g)

[13]

J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180.