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An iterative solution of a variational inequality for certain monotone operators in Hilbert space
Author(s):
Ronald E.
Bruck Jr.
Journal:
Bull. Amer. Math. Soc.
81
(1975),
890-892.
MSC (1970):
Primary 47H05, 47H10
Corrigendum, Volume 81:
Bull. Amer. Math. Soc., Volume 82, Number 2 (1976), 353--353
MathSciNet review:
0383159
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References:
- 1.
- H. Brezis and F. E. Browder, Equations integrales non linéaires du type Hammerstein, C. R. Acad. Sci. Paris SéV. A-B 279 (1974), A1-A2. MR 380534
- 2.
- H. Brezis and F. E. Browder, Some new results about Hammerstein equations. Bull. Amer. Math. Soc. 80 (1974), 567-572. MR 338855
- 3.
- F. E. Browder, Convergence theorems for sequences of nonlinear operators in Banach spaces, Math. Z. 100 (1967), 201-225. MR 35 #5984. MR 215141
- 4.
- F. E. Browder, Nonlinear variational inequalities and maximal monotone mappings in Banach spaces, Math. Ann. 183 (1969), 213-231. MR 42 #6661. MR 271780
- 5.
- F. E. Browder and W. V. Petryshn, Construction of fixed points of nonlinear mappings in Hubert space, J. Math. Anal. Appl. 20 (1967), 197-228. MR 36 #747. MR 217658
- 6.
- R. E. Bruck, Jr., Asymptotic convergence of nonlinear contraction semigroups in Hilbert space, J. Functional Analysis 18 (1975), 15-26. MR 377609
- 7.
- R. E. Bruck, Jr., The iterative solution of the equation $y\in x+Tx$ for a monotone operator T in Hilbert space, Bull. Amer. Math. Soc. 79 (1973), 1258-1261. MR 48 #7034. MR 328692
- 8.
- R. E. Bruck, Jr., A strongly convergent iterative solution of $0\in U(x)$ for a maximal monotone operator U in Hubert space, J. Math. Anal. Appl. 48 (1974), 114-126. MR 361941
- 9.
- A. A. Goldstein, Convex programming in Hilbert space, Bull. Amer. Math. Soc. 70 (1964), 709-710. MR 29 #3262. MR 165982
- 10.
- J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969. MR 41 #4326. MR 259693
- 11.
- 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 211301
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Additional Information:
DOI:
10.1090/S0002-9904-1975-13874-2
PII:
S 0002-9904(1975)13874-2
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