Abstract
For a Banach Space X Garcia-Falset introduced the coefficient R(X) and showed that if R(X) < 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ∥Tx − Ty∥ ≤ a∥x − y∥ + b∥x − Ty∥ for any x, y ∈ X, where a, b ≥ 0, a + b ≤ 1. We show that if \( R{\left( X \right)} < \frac{2} {{1 + b}} \) then T has a fixed point in X.
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Supported by the National Natural Science Foundation of China (No. 10461006), the Natural Science Foundation of Shandong Province (Y002A10) and the Younger Foundation of Yantai University (SX05Z9).
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Wu, Cx., Zhang, Lj. Fixed Points for Mean Non-expansive Mappings. Acta Mathematicae Applicatae Sinica, English Series 23, 489–494 (2007). https://doi.org/10.1007/s10255-007-0388-x
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DOI: https://doi.org/10.1007/s10255-007-0388-x