## On the Mann iterative process

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**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, - 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, - 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,

*Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält*, Studia Math.

**2**(1930), 7-9.

*Averaging iteration in a Banach space*, Notices Amer. Math. Soc.

**15**(1968), 180. Abstract #653-342.

*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