Burton, TheodorePurnaras, Ioannis K.2023-04-172023-04-172022-03-21Burton, T. A., & Purnaras, I. K. (2022). Open mappings: The case for a new direction in fixed point theory. <i>Electronic Journal of Differential Equations, 2022</i>(23), pp. 1-30.1072-6691https://hdl.handle.net/10877/16582Classical 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.Text30 pages1 file (.pdf)enAttribution 4.0 InternationalOpen mappingsProgressive contractionsExistenceUniquenessQuadratic integral equationsArticle