Algorithms for fixed points of nonexpansive operators

Author

• Michael Donald Humphries

Abstract

"Browder proved that in a Hilbert space or a uniformly convex Banach space every non-expansive self-map of a closed, bounded, and convex set has a fixed point. This dissertation contains two algorithms for finding a fixed point of such an operator. The first is a special case of the Mann process. It averages two points which are relatively distant to obtain a better approximation to a fixed point. Under Browder's hypotheses, there is a fixed point which is the limit of a sequence of fixed points of contractions. The second algorithm uses Richardson extrapolation to accelerate the convergence of this sequence. Some results related to fixed point theory are discussed, particularly Brosowski's Theorem in approximation theory"-- Abstract, p. ii

Advisor(s)

Hicks, Troy L.

Committee Member(s)

Kieffer, John C.
Plummer, O. R.
Penico, Anthony J., 1923-2011
Cunningham, David R.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

Fall 1980

Pagination

vi, 46 pages

Note about bibliography

Includes bibliographical references (pages 40-41)

Rights

© 1980 Michael Donald Humphries, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 4595

Print OCLC #

8649459

Recommended Citation

Humphries, Michael Donald, "Algorithms for fixed points of nonexpansive operators" (1980). Doctoral Dissertations. 136.
https://scholarsmine.mst.edu/doctoral_dissertations/136