A new approach to the study of fixed points based on soft rough covering graphs

Imran Shahzad Khan; Nasir Shah; Abdullah Shoaib; Poom Kumam; Kanokwan Sitthithakerngkiet; Imran Shahzad Khan; Nasir Shah; Abdullah Shoaib; Poom Kumam; Kanokwan Sitthithakerngkiet

doi:10.3934/math.20231041

AIMS Mathematics

2023, Volume 8, Issue 9: 20415-20436. doi: 10.3934/math.20231041

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Research article

A new approach to the study of fixed points based on soft rough covering graphs

1.
Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
2.
Department of Mathematics, Islamabad Model College for Girls, F-6/2, Islamabad, Pakistan
3.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Thung Khru, Bangkok 10140, Thailand
4.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand

Received: 13 March 2023 Revised: 05 May 2023 Accepted: 09 May 2023 Published: 25 June 2023
MSC : 05C72, 05C76, 05C85

Mathematical approaches to structure model problems have a significant role in expanding our knowledge in our routine life circumstances. To put them into practice, the right formulation, method, systematic representation, and formulation are needed. The purpose of introducing soft graphs is to discretize these fundamental mathematical ideas, which are inherently continuous, and to provide new tools for applying mathematical analysis technology to real-world applications including imperfect and inexact data or uncertainty. Soft rough covering models $ \left(\text{briefly}, \text{ }\mathcal{SRC}\text{-Models}\right) $, a novel theory that addresses uncertainty. In this present paper, we have introduced two new concepts $ \mathcal{L}\mathfrak{i} $-soft rough covering graphs ($ \mathcal{L}\mathfrak{i} $-$ \mathcal{SRCG} $s) and the concept of fixed point of such graphs. Furthermore, we looked into a some algebras that dealt with the fixed points of $ \mathcal{L}\mathfrak{i} $-$ \mathcal{SRCG} $s. Applications of the algebraic structures available in covering soft sets to soft graphs may reveal new facets of graph theory.
Citation: Imran Shahzad Khan, Nasir Shah, Abdullah Shoaib, Poom Kumam, Kanokwan Sitthithakerngkiet. A new approach to the study of fixed points based on soft rough covering graphs[J]. AIMS Mathematics, 2023, 8(9): 20415-20436. doi: 10.3934/math.20231041

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Abstract

Mathematical approaches to structure model problems have a significant role in expanding our knowledge in our routine life circumstances. To put them into practice, the right formulation, method, systematic representation, and formulation are needed. The purpose of introducing soft graphs is to discretize these fundamental mathematical ideas, which are inherently continuous, and to provide new tools for applying mathematical analysis technology to real-world applications including imperfect and inexact data or uncertainty. Soft rough covering models $ \left(\text{briefly}, \text{ }\mathcal{SRC}\text{-Models}\right) $, a novel theory that addresses uncertainty. In this present paper, we have introduced two new concepts $ \mathcal{L}\mathfrak{i} $-soft rough covering graphs ($ \mathcal{L}\mathfrak{i} $-$ \mathcal{SRCG} $s) and the concept of fixed point of such graphs. Furthermore, we looked into a some algebras that dealt with the fixed points of $ \mathcal{L}\mathfrak{i} $-$ \mathcal{SRCG} $s. Applications of the algebraic structures available in covering soft sets to soft graphs may reveal new facets of graph theory.

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