• Login
  • Help Guide
View Item 
  •   JOOUST IR Home
  • Theses & Dissertations
  • Masters Theses and Dissertations
  • School of Health Sciences
  • View Item
  •   JOOUST IR Home
  • Theses & Dissertations
  • Masters Theses and Dissertations
  • School of Health Sciences
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

On convexity of chebyshev sets in norm-attainable classes

Thumbnail
View/Open
SAM Ndiege THESIS.pdf (265.3Kb)
Publication Date
2023
Author
Owiti, Ndiege Samson
Type
Thesis
Metadata
Show full item record
Abstract/Overview

Best approximation is an interesting field in functional analysis that has attracted a lot of attention from many researchers for a very long period of time up-to-date. Of greatest consideration is the characterization of the Chebyshev set which is a subset of a normed linear space which contains unique best approximations. However, a fundamental question remains unsolved to-date regarding the convexity of the Chebyshev set in infinite normed linear space known as the Chebyshev set problem. The question which has not been answered is: Is every Chebyshev set in a normed linear space convex? This question has not got any solution including the simplest form of a real Hilbert space. The main objective of this study is to characterize Chebyshev sets and convexity in normed linear spaces. The specific objectives include to: Determine conditions under which subsets of normed linear spaces are Chebyshev; Characterize distance functions of Chebyshev set in normed linear spaces and; Investigate convexity of Chebyshev set in normed linear spaces. The methodology involved the use of known fundamental principles like the Bunt-Motzkin Theorem, Fre`chet and Gateaux differentiability conditions and best approximation techniques. The results of this study show that every non-void closed set in N A(H ) is a Chebyshev set if it is Euclidean. Also, if U is proximal in N A(H ) then U is closed and a Chebyshev set. Every distance function of a Chebyshev set of the normed linear space of all norm-attainable real- valued functions is Fr´echet differentiable. For convexity, it has been shown that every PU (ξ) which is convex is a Chebyshev set. The results of this study have provided a partial solution to the Chebyshev set problem and are also useful in solving convex optimization problems.

Subject/Keywords
Chebyshev sets and convexity in normed linear spaces.; Subsets of normed linear spaces.
Publisher
Jooust
Permalink
http://ir.jooust.ac.ke/handle/123456789/14094
Collections
  • School of Health Sciences [46]

Browse

All of JOOUST IRCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

LoginRegister

Statistics

View Usage Statistics

Contact Us

Copyright © 2023-4 Jaramogi Oginga Odinga University of Science and Technology (JOOUST)
P.O. Box 210 - 40601
Bondo – Kenya

Useful Links

  • Report a problem with the content
  • Accessibility Policy
  • Deaccession/Takedown Policy

TwitterFacebookYouTubeInstagram

  • University Policies
  • Access to Information
  • JOOUST Quality Statement