carpathian_2019_35_2_209_220_abstractLet 
be a metric space, 
, 
, with 
, 
. For the fixed point equation
(1) 
we consider the following iterative algorithm,
(2) 
By definition, the algorithm \eqref{equ2} is convergent if,
![\[x_n(x)\to x^*(x)\in F_f\text{ as }n\to\infty,\ \forall\ x\in X.\]](https://www.carpathian.cunbm.utcluj.ro/wp-content/ql-cache/quicklatex.com-73a4cf26beda281a3f85170a93927305_l3.png "Rendered by QuickLaTeX.com")
In this paper we give some conditions on \underline{
and } which imply the convergence of algorithm \eqref{equ2}. In this way we improve some results given in [ Rus, I. A., {\em An abstract point of view on iterative approximation of fixed points: impact on the theory of fixed point equations}, Fixed Point Theory, \textbf{13} (2012), No. 1, 179–192].
In our results, in general we do not suppose that, 
. Some research directions are formulated.
