International Journal of Management and Fuzzy Systems
Volume 6, Issue 3, September 2020, Pages: 53-58
Received: Sep. 16, 2020;
Accepted: Oct. 13, 2020;
Published: Nov. 11, 2020
Views 119 Downloads 17
Dawood Khan, Department of Mathematics, University of Balochistan, Quetta, Pakistan
Abdul Rehman, Department of Mathematics, University of Balochistan, Quetta, Pakistan
Naveed Sheikh, Department of Mathematics, University of Balochistan, Quetta, Pakistan
Saleem Iqbal, Department of Mathematics, University of Balochistan, Quetta, Pakistan
Israr Ahmed, Department of Mathematics, University of Balochistan, Quetta, Pakistan
In the present manuscript we introduce the concept of some notions such as fixed points, periodic points, invariant set and strongly invariant or S-invariant set of discrete dynamical system (Z, Ψ) in BCI-algebra where in (Z, Ψ), Z is a non-empty set and supposed to be a BCI-algebra and the mapping Ψ is a homomorphism from Z to Z and establish some new homomorphic properties of BCI-algebra based on these notions. We also prove some new results related to the set that contains the all fixed points and to the set that contains all periodic points in Z such that we prove that the set of all fixed points and the set of all periodic points in BCI-algebra Z are the BCI-sub algebras. We show that when a sub set of BCI-algebra Z is an invariant set with respect to Ψ. We prove that the set of all fixed points and the set of all periodic points in p-semisimple BCI-algebra Z are the ideals of Z. We also prove that the set of all fixed points in Z is an S-invariant subset of a BCI-algebra Z. We have no doubt that the research along this line can be kept up, and indeed, some results in this manuscript have already made up a foundation for further exploration concerning the further progression of a discrete dynamical system in BCI-algebra and their applications in other disciplines of algebra.
Properties of Discrete Dynamical System in BCI-Algebra, International Journal of Management and Fuzzy Systems.
Vol. 6, No. 3,
2020, pp. 53-58.
Copyright © 2020 Authors retain the copyright of this article.
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