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.
Highlights
In the year 1999, Molodtsov [1]initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties
Research works in soft set theory and its applications in various fields have been rapidly progressed since 2002 until now
Some applications of soft real sets and soft real numbers have been presented in real life problems
Summary
In the year 1999, Molodtsov [1]initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties. He has shown several applications of this theory to solve many practical problems in economics, engineering, social science, medical science, etc. Two different notions of ’soft metric’ are presented in [5,6] and some properties of soft metric spaces are studied in both cases. In [7,8], the authors introduced the notion of soft linear operators in soft normed linear spaces, and soft complex sets and soft complex numbers. The aim of this paper is to introduce new concepts that relates to soft spaces like the soft fixed point concept, soft Picard iteration and soft Mann iteration. We introduce the concepts of stability of soft iteration processes and discuss the stability of these kinds of soft iterations processes with soft contraction operator
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