Document Zbl 0964.47021

Huang, Nan Jing; Cho, Y. J.; Kang, S. M.; Hwang, H. J.

Ishikawa and Mann iterative processes with errors for set-valued strongly accretive and \(\phi\)-hemicontractive mappings. (English) Zbl 0964.47021

Math. Comput. Modelling 32, No. 7-8, 791-801 (2000).

The authors prove some convergence theorems for certain iterations of Ishikawa and Mann type with errors of strongly accretive set-valued mappings.

Reviewer: Jürgen Appell (Würzburg)

Cited in 1 Review

Cited in 1 Document

MSC:

47H04	Set-valued operators
47J25	Iterative procedures involving nonlinear operators
47H06	Nonlinear accretive operators, dissipative operators, etc.

Keywords:

convergence theorems; iterations of Ishikawa and Mann type with errors; strongly accretive set-valued mappings

Cite Review PDF

Full Text: DOI

References:

[1]	Osilike, M. O., Iterative solution of nonlinear equations of φ-strongly accretive type, J. Math. Anal. Appl., 200, 259-271 (1996) · Zbl 0860.65039
[2]	Chidume, C. B.; Osilike, M. O., Fixed point iterative for strictly hemi-contractive maps in uniformly smooth Banach spaces, Numer. Func. Anal. and Optim., 15, 779-790 (1994) · Zbl 0810.47057
[3]	Browder, F. E., Nonlinear mappings of nonexpansive and accretive type in Banach space, Bull. Amer. Math. Soc., 73, 875-882 (1967) · Zbl 0176.45302
[4]	Kato, T., Nonlinear semigroups and evolution equation, J. Math. Soc. Japan, 19, 502-508 (1967) · Zbl 0163.38303
[5]	Ishikawa, S., Fixed points by a new iteration method, (Proc. Amer. Math. Soc., 44 (1974)), 147-150 · Zbl 0286.47036
[6]	Ishikawa, S., Fixed point and iteration of a nonexpansive mapping in a Banach spaces, (Proc. Amer. Math. Soc., 73 (1976)), 65-71 · Zbl 0352.47024
[7]	Mann, W. R., Mean value methods in iteration, (Proc. Amer. Math. Soc., 4 (1953)), 506-510 · Zbl 0050.11603
[8]	Chang, S. S.; Cho, Y. J.; Lee, B. S.; Jung, J. S.; Kang, S. M., Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces, J. Math. Anal. Appl., 224, 149-165 (1998) · Zbl 0933.47040
[9]	Chidume, C. E., An iterative process for nonlinear Lipschitzian strongly accretive mappings in \(L_p\) spaces, J. Math. Anal. Appl., 151, 453-461 (1990) · Zbl 0724.65058
[10]	Chidume, C. E., Approximation of fixed points of strongly pseudo-contractive mappings, (Proc. Amer. Math. Soc., 120 (1994)), 545-551 · Zbl 0802.47058
[11]	Chidume, C. E., Iterative solution of nonlinear equations with strongly accretive operations, J. Math. Anal. Appl., 192, 502-518 (1995) · Zbl 0868.47040
[12]	Deimling, K., Zeros of accretive operators, Manuscript Math, 13, 283-288 (1994)
[13]	Deng, L., On Chidume’s open questions, J. Math. Anal. Appl., 174, 441-449 (1991) · Zbl 0784.47051
[14]	Deng, L., An iterative process for nonlinear Lipschitzian and strongly accretive mappings in uniformly convex and uniformly smooth Banach spaces, Acta Appl. Math., 32, 183-196 (1993) · Zbl 0801.47040
[15]	Deng, L.; Ding, X. P., Iterative approximation of Lipschitz strictly pseudo-contractive mappings in uniformly smooth Banach spaces, Nonlinear Anal. TMA, 24, 981-987 (1995) · Zbl 0827.47041
[16]	Huang, N. J.; Bai, M. R., A perturbed iterative procedure for multi-valued pseudo-contractive mappings and multi-valued accretive mappings in Banach Spaces, Computers Math. Applic., 37, 6, 7-15 (1999) · Zbl 0969.47044
[17]	Liu, L. S., Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl., 194, 114-125 (1995) · Zbl 0872.47031
[18]	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
[19]	Reich, S., An Iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. TMA, 2, 85-92 (1978) · Zbl 0375.47032
[20]	Rhoades, B. E., Comments on two fixed point iteration methods, J. Math. Anal. Appl., 56, 741-750 (1976) · Zbl 0353.47029
[21]	Tan, K. K.; Xu, H. K., Iterative solution to nonlinear equations and strongly accretive operators in Banach spaces, J. Math. Anal. Appl., 178, 9-21 (1993) · Zbl 0834.47048
[22]	Weng, X. L., Fixed point iteration for local strictly pseudo-contractive mappings, (Proc. Amer. Math. Soc., 113 (1991)), 727-731 · Zbl 0734.47042
[23]	Xu, Y. G., Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl., 224, 91-101 (1998) · Zbl 0936.47041
[24]	Zhou, H. Y., Iterative solution of nonlinear equations involving strongly accretive operators without the Lipschitz assumption, J. Math. Anal. Appl., 213, 296-307 (1997) · Zbl 0896.47048
[25]	Zhou, H. Y.; Jia, Y. T., Approximation of fixed points of strongly pseudo-contractive maps without Lipschitz assumption, (Proc. Amer. Math. Soc., 125 (1997)), 1705-1709 · Zbl 0871.47045
[26]	Huang, N. J., On the generalized implicit quasivariational inequalities, J. Math. Anal. Appl., 216, 197-210 (1997) · Zbl 0886.49007
[27]	Petryshyn, W. V., A characterization of strictly convexity of Banach spaces and other uses of duality mappings, J. Func. Anal., 8, 282-291 (1970) · Zbl 0199.44004
[28]	Morales, C. H., Surjectivity theorems for multi-valued mappings of accretive type, Comment. Math. Univ. Carolin., 26, 2, 397-413 (1985) · Zbl 0595.47041
[29]	Nadler, S. B., Multi-valued contraction mappings, Pacific J. Math., 30, 475-488 (1969) · Zbl 0187.45002

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.