Date of Award
Doctor of Philosophy (PhD)
Sufficient conditions are given for a multifunction (set-valued function) to admit a continuously differentiable selection in one dimension. These conditions are given in terms of Clarke generalized gradients of the Hamiltonian associated with the multifunction. Also, the multifunctions in one dimension that can be parametrized with continuously differentiable functions are completely characterized. The characterization is again in terms of Clarke generalized gradients of the Hamiltonian associated with the multifunction.
Knuckles, Craig, "Continuously Differentiable Selections and Parametrizations of Multifunctions in One Dimension." (1995). LSU Historical Dissertations and Theses. 5962.