Characteristic conditions for convergence of generalized steepest descent approximation to multivalued accretive operator equations. (English) Zbl 0957.65048
The main result (Theorem 2.1) gives a characterization of the convergence of the generalized steepest descent approximation method(GSDA) to a zero of a multivalued quasi-accretive operator defined on a real uniformly smooth Banach space.
Reviewer: Vasile Berinde (Baia Mare)
MSC:
65J15 | Numerical solutions to equations with nonlinear operators |
47J25 | Iterative procedures involving nonlinear operators |
Keywords:
Banach space; quasi-accretive operator; generalized steepest descent approximation method; error estimation; convergenceReferences:
[1] | Xu, Z. B.; Roach, G. F., A necessary and sufficient condition for convergence of steepest deacent approximation to accretive operator equations, J. Math. Anal. Appl., 167, 340-354 (1992) · Zbl 0818.47061 |
[2] | Zhou, H. Y., A note on a theorem of Xu and Roach, J. Math. Anal. Appl., 227, 300-304 (1998) · Zbl 0927.47037 |
[3] | Reich, S., An iterative procedure for constructing zeros of accretive sets in Banach space, Nonl. Anal., 2, 85-92 (1978) · Zbl 0375.47032 |
[4] | Browder, F. E., Nonlinear mapping of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc., 73, 875-882 (1967) · Zbl 0176.45302 |
[5] | Kato, T., Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19, 508-520 (1967) · Zbl 0163.38303 |
[6] | Xu, Z. B.; Roach, G. F., Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl., 157, 189-210 (1991) · Zbl 0757.46034 |
[7] | Zhou, H. Y.; Jia, Y. T., Approximating the zeros of accretive operators by the Ishikawa iteration process, Abstr. Appl. Anal., 1, 153-167 (1996) · Zbl 0945.47044 |
[8] | Zhou, H. Y.; Jia, Y. T., Approximation of fixed points of strongly pseudocontractive maps without Lipschitz assumption, (Proc. Amer. Math. Soc., 125 (1997)), 1705-1709 · Zbl 0871.47045 |
[9] | Zhou, H. Y., Iterative solution of nonlinear equations involving strongly accretive operators without Lipschitz assumption, J. Math. Anal. Appl., 213, 296-307 (1997) · Zbl 0896.47048 |
[10] | H.Y. Zhou, A characteristic condition for convergence of steepest descent approximation to accretive operator equations, (submitted).; H.Y. Zhou, A characteristic condition for convergence of steepest descent approximation to accretive operator equations, (submitted). · Zbl 0958.47043 |
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