Document Type : Research Paper


1 Department of Mathematics, Faculty of Science and Arts, Aksaray University, Aksaray Turkey.

2 Department of Mathematical Engineering,Y\i ld\i z Technical University, Davutpasa Campus, Esenler, 34210 Istanbul, Turkey.


In the present paper, we show that $S^*$ iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method  and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. Finally, we obtain a data dependence result for almost contraction mappings by using $S^*$ iteration method and in order to show validity of this result we give an example.


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