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An Existence Theorem for an Integral Equation

The principal theorem of this thesis is a theorem by Peano on the existence of a solution to a certain integral equation. The two primary notions underlying this theorem are uniform convergence and equi-continuity. Theorems related to these two topics are proved in Chapter II. In Chapter III we state and prove a classical existence and uniqueness theorem for an integral equation. In Chapter IV we consider the approximation on certain functions by means of elementary expressions involving "bent line" functions. The last chapter, Chapter V, is the proof of the theorem by Peano mentioned above. Also included in this chapter is an example in which the integral equation has more than one solution. The first chapter sets forth basic definitions and theorems with which the reader should be acquainted.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc503874
Date05 1900
CreatorsHunt, Cynthia Young
ContributorsAppling, William D. L., Bator, Elizabeth M.
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Format42 leaves, Text
RightsPublic, Hunt, Cynthia Young, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved.

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