Journal of the Nigerian Mathematical Society

ULTIMATE BOUNDEDNESS OF SOLUTIONS FOR A CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATION

Daniel Adams — 2024-12-24

Sufficient conditions are established for the ultimate boundedness of solutions for the third order nonlinear differential equation.

ON THE CONNECTEDNESS OF TWO-STEP MARKOV CHAINS AND AN APPLICATION TO PATIENTS’ BEHAVIOUR AND COMPLIANCE WITH MEDICATIONS

Titilola Obilade — 2024-12-24

This paper models tablet consumption from a jar containing single and double units using a two-urn Markov process framework. By solving system equations, it employs statistical measures such as the odds ratio and Cohen's (h) index to characterize variability in compliance among individual patients. The findings demonstrate that a patient's behavior significantly affects the risk of unintended underdose and overdose.

SOME PROPERTIES OF PICTURE FUZZY MULTIRELATIONS

Taiwo Sangodapo — 2024-12-24

This paper investigates into the examination of picture fuzzy multirelations as an extension of picture fuzzy relations. We explore reflexivity, symmetry and transitivity of picture fuzzy multirelations over picture fuzzy multisets, and derive some associated properties.

NEW COMPOSITE RELATIONS CHARACTERIZATION OF STAR-LIKE FINITE SEMIGROUPS

Sulaiman Awwal Akinwunmi — 2024-12-24

The study establishes new star-like classical finite semigroups, provides a cohesive explanation, appraises some combinatorial composite relations on $\alpha\omega_n^*$, and proves some combinatorial relations of star-like $P\omega_n^*$, $T\omega_n^*$, and $O^{cd}P\omega_n^*$ star-like-partial ordered connected transformation semigroups. Let $\alpha\omega_n^*$ be a star-like transformation semigroup with a star-like diskpoint $m^*$, diagonal difference operator $\nabla_{b_{(n, m^*)}}^*$, and vertical difference operator $\Delta_{(n, r^*)}^*$. The study shows that star-like sequences converge uniformly and are reducible if $|\nu^*(\alpha_{(i,j)}^*)| = F(n, \nu^*)$. Also, for a star-like diskpoint $m^*, $ $F(n, m^*) = (n-1)^{2} + (m+1)(n-2)$ and $|\Delta_{(n, r_3^*)}^*| = \lambda_{i}^{2*} + (n - 2) $ such that $|c^{+}(\alpha^*)| \leq |c^{-}(\alpha^*)|$. The new combinatorial composite relations were generated from the existing ones by composition of star-like mapping, which was applied to star-like $\alpha\omega_n^*$ finite semigroups with emphasis on combinatorial triangular arrays.

PRODUCT OF SEMI-TRANSPOSITIONS IN FINITE SEMIGROUP OF INJECTIVE ORDER-PRESERVING TRANSFORMATIONS

Ibrahim Sagir — 2024-12-24

Let $X_n$ be the finite totally ordered set $\{1,2,\cdots,n\}$, $\mathcal{IO}_n$ be the semigroup of all injective order-preserving transformation of $X_n$ and $\mathcal{IO}_{n,r}=\{\alpha\in \mathcal{IO}_n: |im(\alpha)|\leq r\}$ for $(1\leq r\leq n-1)$ be the ideals of injective order-preserving transformations on $X_n$. The semigroup $\mathcal{IO}_{n}$ on $X_n$ is an inverse semigroup and so cannot be generated by its idempotents. In a search for generating set for $\mathcal{IO}_n$ in this article, we identify a class of quasi-idempotents (i.e elements $\alpha$ in $\mathcal{IO}_{n}$ satisfying $\alpha\neq \alpha^2=\alpha^4.$) which we refer to as semi-transpositions and showed that the ideals $\mathcal{IO}_{n,r}$ are generated by semi-trnaspositions. The semi-transposition rank of $\mathcal{IO}_{n,r}$ (defined to be the minimum of such generating set) is obtained to be $2\binom{n}{r}-2.$

BOHR INEQUALITIES FOR SOME GENERALIZED INTEGRAL OPERATORS ON SIMPLY CONNECTED DOMAIN

ISMAILA SESAN AMUSA — 2024-12-24

We obtain the Bohr inequalities for some generalized integral operators of analytic function defined on simply connected domain. Our results are generalizations of some existing results in the literature.

CONVERGENCE OF IMPLICIT NOOR ITERATIVE SEQUENCE TO THE FIXED POINT OF A GENERALIZED NON-EXPANSIVE MAPPING IN UNIFORMLY CONVEX SPACE

Gbenga Akinbo — 2024-12-24

We establish the convergence and stability of an implicit iterative sequence in approximating fixed points of a class of nonexpansive mappings in uniformly convex Banach space and contractive mappings in Banach space. The result obtained is an extension of several others in the literature.