New Proofs of Fixed Point Theorems on Quasi-metric Spaces
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i1.5730Keywords:
Fixed point, quasi-metric space, Banach contraction, Rus-Hicks-Rhoades map, Nadler multimap, Covitz-Nadler multimap, extremal point, stationary pointAbstract
Based on our 2023 Metatheorem in Ordered Fixed Point Theory, we give very simple proofs of known fixed point theorems for various multimap classes on quasi-metric spaces. Such classes are represented by the Banach contractions, the Rus-Hicks-Rhoades maps, the Nadler multimaps, Covitz-Nadler multimaps, and others. Consequently, we obtain simple proofs of a large number of known theorems on extremal elements, fixed points, stationary points for several classes of maps or multimaps. Finally, we add some known theorems for which our Metatheorem does not work.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Sehie Park
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.