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  Partner: UNT Libraries
 Degree Discipline: Mathematics
 Collection: UNT Theses and Dissertations
On Uniform Convergence

On Uniform Convergence

Date: 1951
Creator: Drew, Dan Dale
Description: In this paper, we will be concerned primarily with series of functions and a particular type of convergence which will be described. The purpose of this paper is to familiarize the reader with the concept of uniform convergence. In the main it is a compilation of material found in various references and revised to conform to standard notation.
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Around the Fibonacci Numeration System

Around the Fibonacci Numeration System

Date: May 2007
Creator: Edson, Marcia Ruth
Description: Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.
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Automorphism Groups

Automorphism Groups

Date: August 1965
Creator: Edwards, Donald Eugene
Description: This paper will be concerned mainly with automorphisms of groups. The concept of a group endomorphism will be used at various points in this paper.
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Sequences of Real Numbers

Sequences of Real Numbers

Date: January 1965
Creator: Eskew, Mark F.
Description: The purpose of this thesis is to examine general properties, convergence, and limit points of sequences of real numbers.
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Peripherally Continuous Functions, Graph Maps and Connectivity Maps

Peripherally Continuous Functions, Graph Maps and Connectivity Maps

Date: August 1967
Creator: Evans, Bret Edgar
Description: The purpose of this paper is to investigate some of the more basic properties of peripherally continuous functions, graph maps and connectivity maps.
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Applications in Fixed Point Theory

Applications in Fixed Point Theory

Date: December 2005
Creator: Farmer, Matthew Ray
Description: Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.
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Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces

Strong Choquet Topologies on the Closed Linear Subspaces of Banach Spaces

Date: August 2011
Creator: Farmer, Matthew Ray
Description: In the study of Banach spaces, the development of some key properties require studying topologies on the collection of closed convex subsets of the space. The subcollection of closed linear subspaces is studied under the relative slice topology, as well as a class of topologies similar thereto. It is shown that the collection of closed linear subspaces under the slice topology is homeomorphic to the collection of their respective intersections with the closed unit ball, under the natural mapping. It is further shown that this collection under any topology in the aforementioned class of similar topologies is a strong Choquet space. Finally, a collection of category results are developed since strong Choquet spaces are also Baire spaces.
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A Genesis for Compact Convex Sets

A Genesis for Compact Convex Sets

Date: May 1969
Creator: Ferguson, Ronald D.
Description: This paper was written in response to the following question: what conditions are sufficient to guarantee that if a compact subset A of a topological linear space L^3 is not convex, then for every point x belonging to the complement of A relative to the convex hull of A there exists a line segment yz such that x belongs to yz and y belongs to A and z belongs to A? Restated in the terminology of this paper the question bay be given as follow: what conditions may be imposed upon a compact subset A of L^3 to insure that A is braced?
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Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains

Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains

Date: August 1998
Creator: Finan, Marcel Basil
Description: The aim of this work is the study of the existence and multiplicity of sign changing nonradial solutions to elliptic boundary value problems on annular domains.
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The Laplace Transformation

The Laplace Transformation

Date: August 1965
Creator: Floyd, Russell
Description: A set of definitions, theorems and proofs to describe the Laplace transformation.
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