On algebraic properties of soft real points

Sabir Hussain,Hurmet Fulya Akiz,Amlak Ibrahim Alajlan

doi:10.1186/s13663-019-0659-2

Abstract

In this paper, we introduce and discuss soft single points, which proceed towards soft real points by using real numbers and subsets of set of real numbers. We also define the basic operations on soft real points and explore the algebraic properties. We observe that the set of all soft real points forms a ring. Moreover, we study the soft real point metric using soft real point and explore some of its properties. We then establish a soft real point contraction fixed point theorem using soft real point metric space. It is interesting to mention that these concepts may be helpful for researchers to navigate the ideas put forth in a soft metric extension of several important fixed point theorems for metric spaces deduced from comparable existing results.

Highlights

Soft set theory was proposed by Molodtsov [8], for modelling vagueness and uncertainties, which is inherent in the problems of engineering, physical science, biological science, economics, social science, medical science, etc
The idea of soft single points, which proceed towards soft real points, arose during the study of soft set theory, especially, soft topology and a soft version of the usual topology on real numbers
The existence of soft real points will enable us to define new algebraic and topological structures. These concepts may be helpful for researchers to navigate the ideas put forth in a soft metric extension of several important fixed point theorems for metric spaces deduced from comparable existing results

Summary

Introduction

Soft set theory was proposed by Molodtsov [8], for modelling vagueness and uncertainties, which is inherent in the problems of engineering, physical science, biological science, economics, social science, medical science, etc. Proposition 15 Let (R, + ) is an abelian group and G be set of some soft real points of R.

Results

Conclusion