Fixed points by mean value iterations
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- by Gordon G. Johnson PDF
- Proc. Amer. Math. Soc. 34 (1972), 193-194 Request permission
Abstract:
If E is a convex compact subset of a Hilbert space, T is a strictly pseudocontractive function from E into E and ${x_1}$ is a point in E, then the point sequence $\{ {x_1}\} _{i = 1}^\infty$ converges to a fixed point of T, where for each positive integer n, \[ {x_{n + 1}} = [1/(n + 1)][T{x_n} + n{x_n}].\]References
- 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
- F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228. MR 217658, DOI 10.1016/0022-247X(67)90085-6 J. Schauder, Der fixpunktsatz in funktionalraumen, Studia Math. 2 (1970), 171-180.
- R. L. Franks and R. P. Marzec, A theorem on mean-value iterations, Proc. Amer. Math. Soc. 30 (1971), 324–326. MR 280656, DOI 10.1090/S0002-9939-1971-0280656-9
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 193-194
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291918-4
- MathSciNet review: 0291918