Kwara State University
Risqot Ibrahim-Garba
Designation: Lecturer 1
Department: Statistics and Mathematical Sciences
| My Publications | ||||||||
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| S/N | Title | Abstract | Authors | Volume Numbers | Publication Type | Publication Date | Link | |
| 1 | Some characterizations of equivalence relation on contraction mappings |
Let Tn be the set of full transformations and Pn be the set of partial transformations. It is shown that Tn form a semi-group of order nn and Pn form a semi-group of order (n + 1)n. Let ρ(n, m) be a binary relation then we define the image set of ρ (n, m), I(ρ): {n|n ∈ N and there exists m ∈ M : (m, n) ∈ ρ} whenever (≡ ρ): ≡ ρ on a set M is called an equivalence relation if ≡ ρ is reflexive, symmetric and transitive. Then, For all m ∈ M, we let [m] equivalence class denote the set [m] = {n ∈ M|n ≡ ρm} with respect to ≡ ρ determine by m. Furthermore, we show that D = L ◦ R = R ◦ L = LυR implies L ⊆ J and R ⊆ J . Therefore, D is the minimum equivalence relation class containing L and R. Hence, D ⊆ J . If n ∈ Xm : {n ∈ Xm|n x n = n; nx = xn} then n ∈ Dclass is regular. We also show that for Lclass, Rclass and Hclass for all m, n ∈ D(α) we have α such that D(α) ⊆ M implies I(α) ⊆ M. Then for any transformation of a finite semi-group β,α ∈ S where α = ( 1 2 3 1 2 3 ) and β = ( 1 2 3 3 2 1 ), α and β represent the five equivalence relations and CPn represent the sub-semi-group of partial contraction mapping on M = {1, 2, 3 . . .} while |Q| denotes the order of Q. | S.A. Akinwunmi, M.M. Mogbonju, G.R. Ibrahim | 10 | Journal | 2020-11-01 | https://doi.org/10.1016/j.sciaf.2020.e00643 | |