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Ding, Xie Ping

Iterative process with errors to locally strictly pseudocontractive maps in Banach spaces. (English) Zbl 0930.47037

Comput. Math. Appl. 32, No. 10, 91-97 (1996).
The author studies Mann and Ishikawa iterations for locally pseudocontractive maps in uniformly smooth Banach spaces. This answers some open questions posed in a previous paper by L. Deng and the author [see Appl. Math. Mech., Engl. Ed. 15, 119-123 (1994; Zbl 0812.47066)].
Reviewer: Jürgen Appell (Würzburg)

Cited in 14 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
46B20 Geometry and structure of normed linear spaces

Keywords:

Mann and Ishikawa iterations; locally pseudocontractive maps; uniformly smooth Banach spaces

Citations:

Zbl 0812.47066
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Full Text: DOI

References:

[1] Deng, L.; Ding, X. P., Iterative process for Lipschitz local strictly pseudocontractive mappings, Appl. Math. and Mech., 15, 119-123 (1994) · Zbl 0812.47066
[2] Chidume, C. E., Approximation of fixed points of strongly pseudocontractive mappings, (Proc. Amer. Math. Soc., 120 (1994)), 545-551 · Zbl 0802.47058
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[9] Deng, L.; Ding, X. P., Iterative approximation of Lipschitz strictly pseudocontractive mappings in uniformly smooth Banach spaces, Nonlinear Anal. TMA, 24, 7, 981-987 (1995) · Zbl 0827.47041
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[11] 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
[12] Mann, W. R., Mean value methods in iteration, (Proc. Amer. Math. Soc., 4 (1953)), 506-510 · Zbl 0050.11603
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[14] Reich, S., An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal., 2, 85-92 (1978) · Zbl 0375.47032
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