Year

2025

Season

Spring

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

Committee Chairperson

Raluca Dumitru

Second Advisor

Malgorzata Czerwinska

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Jose Franco

Fourth Advisor

Allan Merino

Department Chair

Richard Patterson

College Dean

Kaveri Subrahmanyam

Abstract

Lipschitz functions on the real line find various applications across mathematics, including in differential equations, optimization, and machine learning. The goal of this thesis is to investigate functions which satisfy certain Lipschitz conditions when ap- plied to operators and matrices. Our study will review two classes of such functions, the class of Operator Lipschitz functions with respect to a given matrix norm, and the class consisting of functions which do not meet Lipschitz conditions in the traditional sense but satisfy inequalities which are Lipschitz in nature – we call such conditions ”Lipschitz-like”. The thesis concludes with a survey of these two categories of results, along with establishing relations between the two.

Download

Share

COinS
 

Accessibility Statement

This item was created or digitized before April 24, 2027, or is a reproduction of legacy material created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the Library provides accessible versions of archival materials by request. If you are experiencing difficulty accessing the information on the site due to a disability, please submit a request through the following form for assistance.