Approximating fixed points of generalized \(\alpha\)-nonexpansive mappings in Banach spaces. (English) Zbl 1367.47069
Summary: We introduce a new type of nonexpansive mappings and obtain a number of existence and convergence theorems. This new class of nonlinear mapping properly contains nonexpansive, Suzuki-type generalized nonexpansive mappings and partially extends firmly nonexpansive and \(\alpha\)-nonexpansive mappings. Also, this class of mapping need not be continuous. Some useful examples are presented to illustrate facts. Some prominent iteration processes are also compared using numerical computations.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
condition (C); generalized \(\alpha\)-nonexpansive mapping; \(\alpha\)-nonexpansive mapping; nonexpansive mapping; Opial property; convergence theoremsReferences:
| [1] | Agarwal R. P., J. Nonlinear Convex Anal. 8 (1) pp 61– (2007) |
| [2] | DOI: 10.1016/j.na.2011.03.057 · Zbl 1238.47036 · doi:10.1016/j.na.2011.03.057 |
| [3] | J. B. Baillon (1979). Quelques aspects de la théorie des points fixes dans les espaces de Banach. I, II. (French) Séminaire d’Analyse Fonctionnelle (1978–1979), Exp. No. 7-8, 45 pp. École Polytech., Palaiseau. |
| [4] | DOI: 10.1073/pnas.53.6.1272 · Zbl 0125.35801 · doi:10.1073/pnas.53.6.1272 |
| [5] | DOI: 10.1073/pnas.54.4.1041 · Zbl 0128.35801 · doi:10.1073/pnas.54.4.1041 |
| [6] | DOI: 10.1090/S0002-9904-1967-11725-7 · Zbl 0161.20103 · doi:10.1090/S0002-9904-1967-11725-7 |
| [7] | DOI: 10.1017/CBO9780511526152 · doi:10.1017/CBO9780511526152 |
| [8] | DOI: 10.1002/mana.19650300312 · Zbl 0127.08005 · doi:10.1002/mana.19650300312 |
| [9] | DOI: 10.1090/S0002-9939-1976-0412909-X · doi:10.1090/S0002-9939-1976-0412909-X |
| [10] | DOI: 10.4134/BKMS.2010.47.5.973 · Zbl 1202.47077 · doi:10.4134/BKMS.2010.47.5.973 |
| [11] | DOI: 10.2307/2313345 · Zbl 0141.32402 · doi:10.2307/2313345 |
| [12] | DOI: 10.1090/S0002-9939-1953-0054846-3 · doi:10.1090/S0002-9939-1953-0054846-3 |
| [13] | Naraghirad E., Fixed Point Theory Appl. (2013) |
| [14] | DOI: 10.1006/jmaa.2000.7042 · Zbl 0964.49007 · doi:10.1006/jmaa.2000.7042 |
| [15] | DOI: 10.1090/S0002-9904-1967-11761-0 · Zbl 0179.19902 · doi:10.1090/S0002-9904-1967-11761-0 |
| [16] | DOI: 10.1017/S0004972700028884 · Zbl 0709.47051 · doi:10.1017/S0004972700028884 |
| [17] | DOI: 10.1090/S0002-9939-1974-0346608-8 · doi:10.1090/S0002-9939-1974-0346608-8 |
| [18] | DOI: 10.1016/j.jmaa.2007.09.023 · Zbl 1140.47041 · doi:10.1016/j.jmaa.2007.09.023 |
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