Olaleru, J.O. and Akewe, H (2007) An Extension of Gregus Fixed Point Theorem. Research Article.
![[img]](http://eprints.covenantuniversity.edu.ng/style/images/fileicons/application_pdf.png) |
PDF
Download (479kB) |
Abstract
Let C be a closed convex subset of a complete metrizable topological vector space (X,d) and T : C → C a mapping that satisfies d(Tx,Ty) ≤ ad(x, y) + bd(x,Tx) + cd(y,Ty) + ed(y,Tx) + f d(x,Ty) for all x, y ∈ C, where 0 < a < 1, b ≥ 0, c ≥ 0, e ≥ 0, f ≥ 0, and a + b + c + e + f = 1. Then T has a unique fixed point. The above theorem, which is a generalization and an extension of the results of several authors, is proved in this paper. In addition, we use the Mann iteration to approximate the fixed point of T. Copyright © 2007 J. O. Olaleru and H. Akewe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |
| Depositing User: | Mrs Patricia Nwokealisi |
| Date Deposited: | 14 Sep 2017 15:37 |
| Last Modified: | 14 Sep 2017 15:37 |
| URI: | http://eprints.covenantuniversity.edu.ng/id/eprint/9314 |
Actions (login required)
 |
View Item |
