Open AccessOn the Soft Stability of Soft Picard and Soft Mann Iteration Processes
Author(s) -
Sabah A. Khaleefah,
Buthainah A. A. Ahmed
Publication year - 2022
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2022.63.2.19
Subject(s) - soft set , mathematics , fixed point iteration , soft materials , stability (learning theory) , contraction (grammar) , calculus (dental) , algebra over a field , fixed point , computer science , pure mathematics , mathematical analysis , artificial intelligence , medicine , materials science , dentistry , machine learning , nanotechnology , fuzzy logic
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.