Date on Master's Thesis/Doctoral Dissertation
8-2017
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Mathematics
Degree Program
Applied and Industrial Mathematics, PhD
Committee Chair
Riedel, Thomas
Committee Member
Powers, Robert
Committee Member
Sahoo, Prasanna
Committee Member
Peters, Susan A.
Author's Keywords
lattices; order; residuated maps; poset; way-below
Abstract
In this dissertation, we will examine residuated mappings on a function lattice and how they behave with respect to the way-below relation. In particular, which residuated $\phi$ has the property that $F$ is way-below $\phi(F)$ for $F$ in appropriate sets. We show the way-below relation describes the separation of two functions and how this corresponds to contraction mappings on probabilistic metric spaces. A new definition for contractions is considered using the way-below relation.
Recommended Citation
Luke, M. Ryan, "Residuated maps, the way-below relation, and contractions on probabilistic metric spaces." (2017). Electronic Theses and Dissertations. Paper 2746.
https://doi.org/10.18297/etd/2746
