Abstract
It is well-known that a partial order induced from a lower semi-continuous map gives us a clear picture of a proof of the Caristi’s fixed point theorem. The proof utilized Zorn’s lemma to guarantee the existence of a minimal element which turns out to be a desired fixed point. The proof cannot be carried over to prove the Brouwer fixed point theorem. We show that making an idea of ordering, we get a proof of the later one.
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Acknowledgements
The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. The first author also would like to thank the Excellence Center in Economics, Chiang Mai University for the support.
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Dedicated to Prof. Hung T. Nguyen for his 75th anniversary
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Dhompongsa, S., Kumam, P. (2021). A Remark on the Caristi’s Fixed Point Theorem and the Brouwer Fixed Point Theorem. In: Kreinovich, V. (eds) Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas. Studies in Computational Intelligence, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-030-45619-1_7
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DOI: https://doi.org/10.1007/978-3-030-45619-1_7
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