Document Type
Report
Source Publication Title
Technical Report 39
Abstract
Let D be a closed subset of a complete metric space (X,p). We seek (i) conditions upon which a map T : D -> X has a fixed point in D and (ii) the construction of an iterative sequence whose limit is a fixed point in D. If X is a Banach space then a classical approach is to set G = I - T and use a numerical search method to minimize ||GX|| in D. Another approach, which does not require a Banach space structure, was recently introduced by Caristi and Kirk ([1],[2]). They prove that a metrically inward contractor map T has a fixed point. Both methods assume conditions which guarantee that for arbitrary x in D there exists y in D such that p(y,Ty) < p(x,TX). This condition is the basis of our study.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
3-1-1976
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Lakshmikantham, V. and Eisenfeld, Jerome, "Fixed Point Theorems on Closed Sets Through Abstract Cones" (1976). Mathematics Technical Papers. 14.
https://mavmatrix.uta.edu/math_technicalpapers/14