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## A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System

#### Dawood KHAN [1] , Abdul REHMAN [2]

In the present manuscript, we introduce the concept of a discrete dynamical system (Ⱬ,Ψ) in BCK-algebra where Ⱬ is a BCK-algebra and Ψ is a homomorphism from Ⱬ to Ⱬ and establish some of their related properties. We prove that the set of all fixed points and the set of all periodic points in BCK-algebra Ⱬ are the BCK-subalgebras. We show that when a subset of BCK-algebra Ⱬ is invariant concerning Ψ. We prove that the set of all fixed points and the set of all periodic points in commutative BCK-algebra Ⱬ with relative cancellation property are the ideals of Ⱬ. We also prove that the set of all fixed points in Ⱬ is an S-invariant subset of a BCK-algebra Ⱬ.
BCK-Algebra, S-invariant or (Strongly invariant) set., discrete dynamical system, periodic points, fixed points, invariant set, strongly invariant
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Primary Language en Mathematics Research Article Orcid: 0000-0002-6850-6783Author: Dawood KHAN (Primary Author)Institution: University of BalochistanCountry: Pakistan Orcid: 0000-0003-2569-8540Author: Abdul REHMANInstitution: University of BalochistanCountry: Pakistan Publication Date : June 30, 2021
 Bibtex @research article { jnt798677, journal = {Journal of New Theory}, issn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2021}, volume = {}, pages = {1 - 10}, doi = {10.53570/jnt.798677}, title = {A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System}, key = {cite}, author = {Khan, Dawood and Rehman, Abdul} } APA Khan, D , Rehman, A . (2021). A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System . Journal of New Theory , (35) , 1-10 . DOI: 10.53570/jnt.798677 MLA Khan, D , Rehman, A . "A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System" . Journal of New Theory (2021 ): 1-10 Chicago Khan, D , Rehman, A . "A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System". Journal of New Theory (2021 ): 1-10 RIS TY - JOUR T1 - A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System AU - Dawood Khan , Abdul Rehman Y1 - 2021 PY - 2021 N1 - doi: 10.53570/jnt.798677 DO - 10.53570/jnt.798677 T2 - Journal of New Theory JF - Journal JO - JOR SP - 1 EP - 10 VL - IS - 35 SN - 2149-1402- M3 - doi: 10.53570/jnt.798677 UR - https://doi.org/10.53570/jnt.798677 Y2 - 2021 ER - EndNote %0 Journal of New Theory A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System %A Dawood Khan , Abdul Rehman %T A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System %D 2021 %J Journal of New Theory %P 2149-1402- %V %N 35 %R doi: 10.53570/jnt.798677 %U 10.53570/jnt.798677 ISNAD Khan, Dawood , Rehman, Abdul . "A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System". Journal of New Theory / 35 (June 2021): 1-10 . https://doi.org/10.53570/jnt.798677 AMA Khan D , Rehman A . A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System. JNT. 2021; (35): 1-10. Vancouver Khan D , Rehman A . A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System. Journal of New Theory. 2021; (35): 1-10. IEEE D. Khan and A. Rehman , "A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System", Journal of New Theory, no. 35, pp. 1-10, Jun. 2021, doi:10.53570/jnt.798677

Authors of the Article
[2]