×

Iterative solutions of nonlinear equations of the strongly accretive type. (English) Zbl 0911.47063

Convergence of Mann iteration process and Ishikawa iteration method are proved under various continuity assumptions on strongly pseudo-contractive mappings in uniformly smooth Banach spaces.
Reviewer: S.Tersian (Russe)

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J05 Equations involving nonlinear operators (general)
47H06 Nonlinear accretive operators, dissipative operators, etc.
46B20 Geometry and structure of normed linear spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bethke, Naturwiss Fak. 27 pp 263– (1989)
[2] Browder, Amer. Math. Soc. 73 pp 875– (1967)
[3] Browder, J. Math. Anal. Appl. 20 pp 197– (1967)
[4] Bruck, Bull. Amer. Math. Soc. 79 pp 1258– (1973)
[5] Carbone, Jnanabha 20 (1990)
[6] : The Fixed Point Theory for Mappings Satisfying Inwardness Conditions, Ph. D dissertation, University of Iowa, 1975
[7] Chidume, J. Math. Anal. Appl. 116 pp 531– (1986)
[8] Chidume, Amer. Math. Soc. 99 pp 283– (1987)
[9] Chidume, Austral. Math. Soc. 42 pp 21– (1990)
[10] Chidume, J. Math. Anal. Appl. 151 pp 2– (1990)
[11] Chidume, Approximation of Fixed Points of Strongly Pseudo-Contractive Mappings, Proc. Amer. Math. Soc. 120 pp 545– (1994) · Zbl 0802.47058
[12] Chidume, Funct. Anal. Optim. 15 pp 779– (1994)
[13] Deimling, Manuscripta Math. 13 pp 365– (1974)
[14] Hicks, J. Math. Anal. Appl. 59 pp 498– (1977)
[15] Ishikawa, Amer. Math. Soc. 149 pp 147– (1974) · doi:10.1090/S0002-9939-1974-0336469-5
[16] Ishikawa, Amer. Math. Soc. 73 pp 65– (1976) · doi:10.1090/S0002-9939-1976-0412909-X
[17] Kato, J. Math. Soc. Japan 18/19 pp 508– (1967)
[18] Kirk, Manuscripta Math. 30 pp 89– (1979)
[19] Kirk, Math. Bull. 24 pp 441– (1981) · Zbl 0475.47041 · doi:10.4153/CMB-1981-067-0
[20] Mann, Amer. Math. Soc. 4 pp 506– (1953)
[21] Martin, Amer. Math. Soc. 26 pp 307– (1970)
[22] Mukerjee, J. Pure Appl. Math. 15 pp 276– (1966)
[23] Reich, J. Math. Anal. Appl. 75 pp 287– (1980)
[24] : Constructive Techniques for Accretive and Monotone Operators, in Applied Nonlinear Analysis, Academic Press, New York, 335–345, 1979
[25] Bruck, Nonlinear Analysis 4 pp 939– (1980)
[26] Nevanlinna, J. Math. 32 pp 44– (1979)
[27] Rhoades, J. Math. Anal. Appl. 56 pp 741– (1976)
[28] Rockafellar, J. 16 pp 397– (1969)
[29] Schu, Math. Nachr. 153 pp 313– (1991)
[30] Schu, Applicable Analysis 40 pp 67– (1991)
[31] Weng, Amer. Math. Soc. 113 pp 727– (1991)
[32] Xu, Nonlinear Anal. 16 pp 1127– (1991)
[33] Tan, J. Math. Anal. Appl. 178 pp 9– (1993)
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.