  In this paper, we introduce a new iteration method and show that this
iteration method can be used to approximate fixed point of almost contraction
mappings. Furthermore, we prove that the new iteration method is equivalent to
both Mann iteration method and Picard-Mann hybrid iteration method and also
converges faster than Picard-Mann hybrid iteration method for the class of
almost contraction mappings. In addition to these we give a table and graphics
for support this result. Finally, we prove a data dependence result for almost
contraction mappings by using the new iteration method.
