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Strong convergence theorems for resolvents of accretive operators in Banach spaces. (English) Zbl 0437.47047

47J25Iterative procedures (nonlinear operator equations)
47H06Accretive operators, dissipative operators, etc. (nonlinear)
47H09Mappings defined by “shrinking” properties
47J05Equations involving nonlinear operators (general)
65J15Equations with nonlinear operators (numerical methods)
Full Text: DOI
[1] Baillon, J. -B: Générateurs et semi-groupes dans LES espaces de Banach uniformément lisses. J. functional analysis 29, 199-213 (1978) · Zbl 0386.47039
[2] J.-B. Baillon, personal communication, 1979.
[3] Bakus\breve{}inskii, A. B.; Poljak, B. T.: On the solution of variational inequalities. Soviet math. Dokl. 15, 1705-1710 (1974) · Zbl 0311.49015
[4] Browder, F. E.: Nonlinear operators and nonlinear equations of evolution in Banach spaces. Proc. symp. Pure math. 18 (1976) · Zbl 0327.47022
[5] Bruck, R. E.: A strongly convergent iterative solution of O $\epsilon U$ (x) for a maximal monotone operator U in Hilbert space. J. math. Anal. appl. 48, 114-126 (1974) · Zbl 0288.47048
[6] Grandall, M. G.; Pazy, A.: Semigroups of nonlinear contractions and dissipative sets. J. functional analysis 3, 376-418 (1969) · Zbl 0182.18903
[7] Gwinner, J.: On the convergence of some iteration processes in uniformly convex Banach spaces. Proc. amer. Math. soc. 71, 29-35 (1978) · Zbl 0393.47040
[8] Halpern, B.: Fixed points of non-expanding maps. Bull. amer. Math. soc. 73, 957-961 (1967) · Zbl 0177.19101
[9] Lions, P. -L: Approximation de points fixes de contractions. C. R. Acad. sci. Paris 284, 1357-1359 (1977) · Zbl 0349.47046
[10] Nevanlinna, O.: Global iteration schemes for monotone operators. MRC report no. 1862 (1978) · Zbl 0439.47043
[11] Reich, S.: Asymptotic behavior of contractions in Banach spaces. J. math. Anal. appl. 44, 57-70 (1973) · Zbl 0275.47034
[12] Reich, S.: Some fixed point problems. Atti accad. Naz. lincei 57, 194-198 (1974) · Zbl 0329.47019
[13] Reich, S.: Approximating zeros of accretive operators. Proc. amer. Math. soc. 51, 381-384 (1975) · Zbl 0294.47042
[14] Reich, S.: Asymptotic behavior of semigroups of nonlinear contractions in Banach spaces. J. math. Anal. appl. 53, 277-290 (1976) · Zbl 0337.47027
[15] Reich, S.: Extension problems for accretive sets in Banach spaces. J. functional analysis 26, 378-395 (1977) · Zbl 0378.47037
[16] Reich, S.: Almost convergence and nonlinear ergodic theorems. J. approximation theory 24, 269-272 (1978) · Zbl 0404.47032
[17] Reich, S.: An iterative procedure for constructing zeros of accretive sets in Banach spaces. Nonlinear analysis 2, 85-92 (1978) · Zbl 0375.47032
[18] Reich, S.: Iterative methods for accretive sets. Nonlinear equations in abstract spaces, 317-326 (1978)
[19] Reich, S.: Weak convergence theorems for nonexpansive mappings in Banach spaces. J. math. Anal. appl. 67, 274-276 (1979) · Zbl 0423.47026
[20] Reich, S.: Constructive techniques for accretive and monotone operators. Applied nonlinear analysis, 335-345 (1979)
[21] Reich, S.: Constructing zeros of accretive operators, II. Applicable analysis 9, 159-163 (1979) · Zbl 0424.47034
[22] Reich, S.: Product formulas, nonlinear semigroups, and accretive operators. J. functional analysis 36, 147-168 (1980) · Zbl 0437.47048
[23] S. Reich, Asymptotic behavior of resolvents in Banach spaces, Atti Accad. Naz. Lincei, in press · Zbl 0462.47049