This article deals with -fixed points of operators on metric spaces (a point from a metric space is called an -fixed one if , the set of such points is denoted by ). The first statement of this article is an evident conclusion
The second one estimates provided that satisfies the condition
in this case, the inequality holds. In the main part of the article, these simple statements apply when is a usual contraction, when satisfies the Kannan condition , , when satisfies the Chatterjea condition , , when satisfies the Zamfirescu condition , , , and at last, when satisfies condition , , (Theorems 2.5 and 3.5); this last condition was offered by V. Berinde. In all these cases, the function is calculated.