Strong convergence of three step iteration process for nonexpansive and strongly pseudocontractive mappings. (English) Zbl 1438.47133
Summary: In this paper, we introduce a three step iteration process and prove a strong convergence theorem for finding the common fixed point associated with nonexpansive and strongly pseudocontractive mappings in real uniformly smooth Banach space. A numerical example is given in support of our result. We remark that the iteration process of S. M. Kang et al. [J. Appl. Math. 2013, Article ID 705814, 4 p. (2013; Zbl 1266.47095)] can be obtained as a particular case of our iteration process. In our result the necessity of condition (C) is not required to prove strong convergence.
MSC:
| 47J26 | Fixed-point iterations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
fixed point; nonexpansive mapping; strongly pseudocontractive mapping; uniformly smooth Banach space; strong convergenceCitations:
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