1. Fixed points of functions with max-weighted quasi-arithmetic mean operator.
- Author
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Wen, Ching-Feng, Liu, Chia-Cheng, and Lur, Yung-Yih
- Subjects
- *
FIXED point theory , *ARITHMETIC mean , *OPERATOR theory , *CONTINUOUS functions , *MONOTONE operators , *MATRICES (Mathematics) , *MATHEMATICAL sequences - Abstract
Abstract: Let and f be a continuous, strictly monotone real-valued function. The weighted quasi-arithmetic mean of two numbers a, b is defined by . Let be an real matrix and . We construct a function by for all . In this paper we show that has a unique fixed point . Moreover, it can be shown that for each the sequence , generated by the following iterative scheme: and for all , converges to the unique fixed point . Besides, some properties of the fixed point are derived. As an application, our results imply that the max-weighted quasi-arithmetic mean powers of any matrix are always convergent. The continuity of the function defined by is proposed as well. [Copyright &y& Elsevier]
- Published
- 2014
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