Electron. J. Differential Equations, Vol. 2022 (2022), No. 23, pp. 1-30.

Open mappings: The case for a new direction in fixed point theory

Theodore A. Burton, Ioannis K. Purnaras

Classical fixed point theorems often begin with the assumption that we have a mapping P of a closed convex set in a Banach space G into itself. It then adds a number of conditions which will ensure that there is at least one fixed point in the set G. We continue two earlier studies in which we now propose to stop the process after we have mapped G not only into itself, but into its interior. We then study what we may deduce from this alone.

Submitted October 15, 2020. Published March 21, 2022.
Math Subject Classifications: 34A08, 45D05, 45G05, 47H09, 47H10.
Key Words: Open mappings; progressive contractions; existence; uniqueness; quadratic integral equations.
DOI: https://doi.org/10.58997/ejde.2022.23

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Theodore A. Burton
Northwest Research Institute, 732 Caroline St.
Port Angeles, WA 98362, USA
email: taburton@olypen.com
Ioannis K. Purnaras
Department of Mathematics
University of Ioannina, 451 10
Ioannina, Greece
email: ipurnara@uoi.gr

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