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Inchan, Issara; Plubtieng, Somyot

Approximating solutions for the systems of strongly accretive operator equations. (English) Zbl 1131.47310

Comput. Math. Appl. 53, No. 9, 1317-1324 (2007).
This paper studies the strong convergence of a multi-step iteration scheme to a common fixed point of a finite family of strongly pseudo-contractive mappings.
Reviewer: Stepan Agop Tersian (Rousse)

Cited in 2 Reviews
Cited in 1 Document

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
47H06 Nonlinear accretive operators, dissipative operators, etc.
65J15 Numerical solutions to equations with nonlinear operators

Keywords:

Ishikawa iteration; Mann iteration; multistep iteration; common fixed point; strongly accretive operator; uniformly smooth Banach space
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References:

[1] Browder, F. E., Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc., 73, 875-882 (1967) · Zbl 0176.45302
[2] Browder, F. E., Nonlinear operations and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math., 18, 2 (1976) · Zbl 0176.45301
[3] Chidume, C. E., Approximation of fixed point of strongly pseudocontractive mappings, Proc. Amer. Math. Soc., 120, 545-551 (1994) · Zbl 0802.47058
[4] Chidume, C. E., Convergence theorems for strongly pseudo- contractive and strongly accretive maps, J. Math. Anal. Appl., 228, 254-264 (1998) · Zbl 0927.47035
[5] Chidume, C. E.; Osilike, M. O., Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings, J. Math. Anal. Appl., 192, 727-741 (1995) · Zbl 0862.47045
[6] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0559.47040
[7] Deng, L., An Iterative process for nonlinear Lipschizian and strongly accretive mappings in uniformly convex and uniformly smooth Banach spaces, Acta Appl. Math., 32, 183-196 (1993) · Zbl 0801.47040
[8] Deng, L.; Ding, X. P., Iterative approximation of Lipschiz strictly pseudo-contractive mappings in uniformly smooth Banach spaces, Nonlinear Anal., 24, 981-987 (1995) · Zbl 0827.47041
[9] Glowinski, R.; Tallec, P. Le., Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics (1989), SIAM: SIAM Philadelphia · Zbl 0698.73001
[10] Haiyun, Z.; Yuting, J., Approximation of fixed points of strongly pseudocontractive maps without Lipschitz assumption, Proc. Amer. Math. Soc., 125, 1705-1709 (1995) · Zbl 0871.47045
[11] Ishikawa, S., Fixed point and iteration of a nonexpansive mappings in a Banach spaces, Proc. Amer. Math. Soc., 73, 65-71 (1976) · Zbl 0352.47024
[12] Kato, T., Nonlinear semigroups and evolution equation, J. Math. Soc. Japan, 19, 502-508 (1967) · Zbl 0163.38303
[13] Liu, L. S., Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl., 194, 114-125 (1995) · Zbl 0872.47031
[14] Mann, W. R., Mean value methods in iteration, Proc. Amer. Math. Soc., 4, 506-510 (1953) · Zbl 0050.11603
[15] Martin, R. H., Differential equation on closed subsets of Banach space, Trans. Amer. Math. Soc., 179, 399-414 (1973) · Zbl 0293.34092
[16] Noor, M. A., Three-step iterative algorithms for multivalued quasi variational inclusions, J. Math. Anal. Appl., 255, 589-604 (2001) · Zbl 0986.49006
[17] Noor, M. A.; Rassias, T. M.; Huang, Z., Three-step iterations for nonlinear accretive operator equations, J. Math. Anal. Appl., 274, 59-68 (2002) · Zbl 1028.65063
[18] Osilike, M. O., Iterative solution of nonlinear equations of the \(\phi \)-strongly accretive type, J. Math. Anal. Appl., 200, 259-271 (1996) · Zbl 0860.65039
[19] Osilike, M. O., Ishikawa and Mann iteration methods with errors for nonlinear equations of the accretive type, J. Math. Anal. Appl., 213, 91-105 (1997) · Zbl 0904.47056
[20] Plubteing, S.; Wangkeeree, R., Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces, J. Math. Anal. Appl., 321, 10-23 (2006) · Zbl 1095.47042
[21] Tan, K. K.; Xu, H. K., Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces, J. Math. Anal. Appl., 178, 9-21 (1993) · Zbl 0834.47048
[22] Xu, Y., Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl., 224, 91-101 (1998) · Zbl 0936.47041
[23] Zhou, H., Some convergence theorems for the Ishikawa iterative sequences of certain nonlinear operators in uniformly smooth Banach spaces, Acta Math. Sinica, 40, 751-758 (1997) · Zbl 0922.47060
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