On the convergence and data dependence results for multistep Picard-Mann iteration process in the class of contractive-like operators

Abstract

In this paper, we introduce a new iteration process and prove the convergence of this iteration process to a fixed point of contractive-like operators. We also present a data dependence result for such mappings. Our results unify and extend various results in the existing literature.

Some convergence, stability and data dependency results for a Picard-S iteration method of quasi-strictly contractive operators

“…Pertaining to the iteration methods employed in [1], [6], [8], [9], [12], [17], [21], [20], [19], [23], [24], [25], [29] and [31], it is the usual practice to impose some conditions (α n + β n ) = ∞, 0 < α α n , 0 < β β n , β n α n , 1 2 α n , 1 2 α n (1 − δ) for all n ∈ N on the parametric sequences {α n } ∞ n=0 , {β n } ∞ n=0 , {γ n } ∞ n=0 ⊆ [0, 1] for the type of convergency, stability and data dependency problems considered in those papers. However, none of these conditions has been used in our corresponding results.…”