An iff fixed point criterion for continuous self-mappings on a complete metric space |
| |
Authors: | J Jachymski |
| |
Institution: | (1) Institute of Mathematics, Technical University of od, Zwirki 36, PL-90-924 od, Poland |
| |
Abstract: | Summary Letf be a self-map on a metric space (X, d). We give necessary and sufficient conditions for the sequences {f
n
x} (x X) to be equivalent Cauchy. As a typical application we get the following result. Letf be continuous and (X, d) be complete. If, for anyx, y X d(f
n
x, f
n
y) 0 and for somec > 0, this convergence is uniform for allx, y inX withd(x, y) c thenf has a unique fixed pointp, andf
n
x p, for eachx inX.
This theorem includes among others results of Angelov, Browder, Edelstein, Hicks and Matkowski. |
| |
Keywords: | Primary 47H10 54H25 |
本文献已被 SpringerLink 等数据库收录! |
|