A unified fixed point result along with error estimation and propagation in the fixed point iteration. (English) Zbl 1518.54028
A fixed point result is obtained for a mapping acting in a metric space equipped with a binary relation under a contractive condition using a simulation function and a rational expression. Under an additional condition, the uniqueness of the fixed point is obtained. The results are illustrated by an example and it is shown that the error of \(n\)-th iteration diminishes with \(n\).
Reviewer: Zoran Kadelburg (Beograd)
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 47H10 | Fixed-point theorems |
| 54H10 | Topological representations of algebraic systems |
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