Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces
© Z. Gu and Y. Li. 2008
Received: 17 October 2007
Accepted: 2 January 2008
Published: 15 January 2008
1. Introduction and Preliminaries
where , . The recursion formulas (1.2) were first introduced in 1994 by Rashwan and Saddeek  in the framework of Hilbert spaces.
In recent years, several authors (see [2–6]) have studied the convergence of iterations to a common fixed point for a pair of mappings. Rashwan has studied the convergence of Mann iterations to a common fixed point (see ) and proved that the Ishikawa iterations converge to a unique common fixed point in Hilbert spaces (see ). Recently, Ćirić has proved that if the sequence of Ishikawa iterations sequence associated with and converges to , then is the common fixed point of and (see ). In [4, 6], the authors studied the same problem. In , Bose defined the pair of mean nonexpansive mappings, and proved the existence of the fixed point in Banach spaces. In particular, he proved the following theorem.
Theorem 1.1 ().
It is our purpose in this paper to consider an iterative scheme, which converges to a common fixed point of the pair of mean nonexpansive mappings. Theorem 2.1 extends and improves the corresponding results in .
2. Main Results
Now we prove the following theorem which is the main result of this paper.
The work was partially supported by the Emphases Natural Science Foundation of Guangdong Institution of Higher Learning, College and University (no. 05Z026).
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