Abstract
In this paper we study the following problems: I. Let (M, d) be a complete metric space and f, g : M → M be two operators. We suppose that:
(a) f is a Picard operator with its unique fixed point x *f;
(b) there exists η > 0 such that d(f(x), g(x)) ≤ η, for every x ∈ M.
The problem consists in estimating d(gn(x), x*f), for x ∈ M and n ∈ *.
II. Let B be a Banach space and f, g : B → B be two operators. We suppose that f is a Picard operator. The problem is to find sufficient conditions which guarantee that f + g is a Picard operator.