On the Soft Stability of Soft Picard and Soft Mann Iteration Processes

Abstract

In this paper, we introduce new concepts that relates to soft space based on work that was previously presented by researchers in this regard. First we give the definition of Soft Contraction Operator and some examples. After that we introduce the concepts of soft Picard iteration and soft Mann iteration processes. We also give some examples to illustrate them.
 Many concepts in normed spaces have been generalized in soft normed spaces. One of the important concepts is the concept of stability of soft iteration in soft normed spaces. We discuss this concept by giving some lemmas that are used to prove some theorems about stability of soft iteration processes (with soft contraction operator) with soft Picard iteration procedure as well as soft Mann iteration procedure.