Some results for uniformly \(L\)-Lipschitzian mappings in Banach spaces. (English) Zbl 1163.47308
Summary: The purpose of this work is to prove a strong convergence theorem for a pair of uniformly \(L\)-Lipschitzian mappings in Banach spaces. The results presented in the work improve and extend some recent results of S.S.Chang [Proc.Am.Math.Soc.129, No.3, 845–853 (2001; Zbl 0968.47017)], Y.J.Cho, J.I.Kang and H.–Y.Zhou [Bull.Korean Math.Soc.42, No.4, 661–670 (2005; Zbl 1107.47053)], E.U.Ofoedu [J. Math.Anal.Appl.321, No.2, 722–728 (2006; Zbl 1109.47061)], J.Schu, [J. Math.Anal.Appl.158, No.2, 407–413 (1991; Zbl 0734.47036)] and L.–C.Zeng [Chin.Ann.Math., Ser.A 26, No.2, 283–290 (2005; Zbl 1139.47330); Acta Math.Sci., Ser.A, Chin.Ed.23, No.1, 31–37 (2003; Zbl 1064.47071)].
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
asymptotically pseudo-contractive mapping; normalized duality mapping; uniformly \(L\)-Lipschitzian mapping; fixed point; Banach spaceCitations:
Zbl 0968.47017; Zbl 1107.47053; Zbl 1109.47061; Zbl 0734.47036; Zbl 1139.47330; Zbl 1064.47071References:
| [1] | Chang, S. S., Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 129, 845-853 (2001) · Zbl 0968.47017 |
| [2] | Chang, S. S., On Chidume’s open questions and approximation solutions of multi-valued strongly accretive mapping equation in Banach spaces, J. Math. Anal. Appl., 216, 94-111 (1997) · Zbl 0909.47049 |
| [3] | Cho, Y. J.; Kang, J. I.; Zhou, H. Y., Approximating common fixed points of asymptotically nonexpansive mappings, Bull. Korean Math. Soc., 42, 661-670 (2005) · Zbl 1107.47053 |
| [4] | Gobel, K.; Kirk, W. A., A fixed points theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35, 171-174 (1972) · Zbl 0256.47045 |
| [5] | Moore, C.; Nnoli, B. V., Iterative solution of nonlinear equations involving set-valued uniformly accretive operators, Comput. Math. Appl., 42, 131-140 (2001) · Zbl 1060.47511 |
| [6] | Ofoedu, E. U., Strong convergence theorem for uniformly \(L\)-Lipschitzian asymptotically pseudocontractive mapping in a real Banach space, J. Math. Anal. Appl., 321, 722-728 (2006) · Zbl 1109.47061 |
| [7] | Schu, J., Iterative construction of fixed point of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158, 407-413 (1991) · Zbl 0734.47036 |
| [8] | Zeng, L. C., On the iterative approximation for asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces, Chinese Math. Ann., 26, 283-290 (2005), (in Chinese) · Zbl 1139.47330 |
| [9] | Zeng, L. C., On the approximation of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta Math. Sci., 23, 31-37 (2003), (in Chinese) · Zbl 1064.47071 |
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