An iterative process for nonlinear monotonic nonexpansive operators in Hilbert space
W. G. Dotson
Math. Comp. 32 (1978), 223-225
Primary 47H15; Secondary 65J05
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Abstract: The following theorem is proved: Suppose H is a complex Hilbert space, and is a monotonic, nonexpansive operator on H, and . Define by for all . Suppose for all and diverges. Then the iterative process converges to the unique solution of the equation .
G. Dotson Jr., On the Mann iterative
process, Trans. Amer. Math. Soc. 149 (1970), 65–73. MR 0257828
(41 #2477), http://dx.doi.org/10.1090/S0002-9947-1970-0257828-6
W. Groetsch, A note on segmenting Mann iterates, J. Math.
Anal. Appl. 40 (1972), 369–372. MR 0341204
E. H. ZARANTONELLO, Solving Functional Equations by Contractive Averaging, Technical Report No. 160, U. S. Army Math. Res. Center, Madison, Wisc., 1960.
H. Zarantonello, The closure of the numerical range contains the
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0229079 (37 #4657)
- W. G. DOTSON, JR., "On the Mann iterative process," Trans. Amer. Math. Soc., v. 149, 1970, pp. 65-73. MR 0257828 (41:2477)
- C. W. GROETSCH, "A note on segmenting Mann iterates," J. Math. Anal. Appl., v. 40, 1972, pp. 369-372. MR 0341204 (49:5954)
- E. H. ZARANTONELLO, Solving Functional Equations by Contractive Averaging, Technical Report No. 160, U. S. Army Math. Res. Center, Madison, Wisc., 1960.
- E. H. ZARANTONELLO, "The closure of the numerical range contains the spectrum," Pacific J. Math., v. 22, 1967, pp. 575-595. MR 37 #4657. MR 0229079 (37:4657)
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