Open mappings: The case for a new direction in fixed point theory
Date
2022-03-21
Authors
Burton, Theodore
Purnaras, Ioannis K.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Open mappings, Progressive contractions, Existence, Uniqueness, Quadratic integral equations
Citation
Burton, 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.
Rights
Attribution 4.0 International