International Journal of Mathematical Sciences and Optimization: Theory and Applications

Approximating Fixed Point of Generalized C-class Contractivity Conditions

O. J. Omidire — 2025-01-03

In this study, we introduced novel class of contractivity conditions called C-class Akram contraction and C-class generalized MJ−Contraction and established the convergence of Picard and Jungck iterations to the unique fixed point and unique common fixed point respectively. Our results generalizes and extends some existing related results in literature.

On the Digraphic Decomposition of Stable Quasi-Idempotents within Finite Partial Transformation Semigroups

A. M. Babayo — 2025-01-15

This study explores the universal classification of elements in the finite partial transformation semigroup Pn on the set Xn+1 = {0, 1, 2, . . . , n}. The primary focus is on the interplay between the powers of transformations, equivalence relations, and their cyclic and quasi-idempotent structures. A key observation is that for any transformation α ∈ Pn, repeated application stabilizes, leading to a periodic behavior characterized by the (m, r)-path cycle—a notation capturing both cyclic and linear components of α. To further analyze α, the concept of orbits is introduced, defined as equivalence classes under the relation x ∼ y if xαm = yαr. These orbits provide a framework for understanding the dynamics of α. The study also examines specific elements like idempotents (ε2 = ε) and quasi-idempotents (ξ2 ̸= ξ, ξ4 = ξ2), offering classifications based on the sizes of their cyclic portions within their orbits. A notable result is that stable quasi-idempotents generate the ideal Pn\Sn, where Sn denotes the symmetric group. This work contributes a digraphic characterization of Pn, advancing the understanding of its algebraic structure. The findings have potential applications in semigroup theory, automata, and computational mathematics, particularly in analyzing transformation systems with finite
domains.

Bivariate BCI Algebras

E. Ilojide — 2025-01-15

In this paper, the concept of bivariate BCI algebras is introduced. Properties of ρ- variate, λ- variate and bivariate BCI algebras are investigated.

The equivalence of some iteration schemes with their errors for uniformly continuous strongly successively pseudo-contractive operators

M. O. Odumosu — 2025-02-28

Some iteration schemes may converge faster for certain types of functions or structures in
an arbitrary space. In this paper, we show that the convergence of modified Mann iteration,
modified Mann iteration with errors, modified Ishikawa iteration, modified Ishikawa iteration
with errors, modified Noor iteration, modified Noor iteration with errors, modified multistep
iteration and modified multistep iteration with errors are equivalent for uniformly continuous
strongly successively pseudo-contractive maps in an arbitratry real Banach space. The results
generalize and extend the results of several authors, including Huang and Bu [1], Rhoades and
Soltuz [2–4] and improve the results of Huang et al. [5].

Improved Finite Difference Methods for Solving Second-Order Boundary Value Problems of Ordinary Differential Equations Using Chebyshev Polynomials

E. N. Enemoh — 2025-03-10

In this paper, two advance numerical techniques for solving second-order boundary value problems in ordinary differential equations (ODEs) are presented. The first method, the Chebyshev
Finite Difference Method (CFDM), which enhances the traditional Finite Difference Method
by utilizing Chebyshev Polynomials as basis functions, resulting in improved computational
performance. The second method developed is the Perturbed Chebyshev Finite Difference
Method (Perturbed CFDM), which incorporates perturbation techniques to further enhance
the accuracy and efficiency of the method. Both methods were applied to homogeneous and
non-homogeneous linear boundary value problems, with numerical results demonstrating that
the Perturbed CFDM significantly outperforms both standard CFDM and the traditional finite
difference method in terms of accuracy and computational efficiency. These findings establish
the Perturbed CFDM as a powerful and reliable tool for solving boundary value problems. All
computations were carried out using MATLAB, ensuring accurate approximation and numerical solutions of the tested problems.

Equivalence of the Convergences of some Modified Iterations with Errors for Uniformly Lipschitzian Asymtotically Pseudo-Contractive Maps

M. O. Odumosu — 2025-03-15

Certain iterative schemes demonstrate a faster convergence to a fixed point compared to others when used to solve various nonlinear differential equations. We show that the convergence of various iterative schemes, including the modified Mann iteration, modified Mann iteration with errors, modified Ishikawa iteration, modified Ishikawa iteration with errors, modified Noor iteration, modified Noor iteration with errors, modified multistep iteration and modified multi-step iteration with errors are all equivalent when applied to uniformly Lipschitzian asymptotically pseudo-contractive maps in an arbitrary real Banach space. Our results expand and generalize the earlier works of Rhoades and Soltuz [1], Olaleru and Odumosu [2] and Odumosu, Olaleru and Ayodele [3].

Multiple Regression Analysis of the Impact of some Selected Macro - Economic Variables on the Gross Domestic Product (GDP)

U. Okorafor — 2025-03-15

The economy of many nations is dwindling with the recent happenings in the globe. This development has made macro-economic variables unpredictable and volatile. Understanding the
interrelationships between GDP and key macroeconomic variables is pivotal for navigating economic challenges, fostering sustainable growth, and enhancing overall economic stability. This
study employs multiple linear regression analysis to investigate the relationship between Gross
Domestic Product (GDP) as the dependent variable and four prominent macroeconomic indicators namely, inflation rate, interest rate, exchange rate, and the all- share index as independent
variables. Utilizing a robust dataset spanning historical records of GDP and corresponding data
on inflation rates, interest rates, exchange rates, and stock market performance, this research
evaluated the quantitative impact and significance of these variables on GDP. The model obtained is GDP = 22.995˘0.265INF + 2.452INT + 0.75EX −0.323ASI.. The analysis revealed
compelling results that indicate a statistically significant relationship between GDP and the
selected macroeconomic factors. The findings suggested that inflation rate, interest rate, and
exchange rate exhibit varying degrees of influence on GDP, with inflation rate demonstrating a
moderately negative impact, while interest rate and exchange rate display positive associations
with GDP fluctuations. It is recommended that policymakers should consider adopting measures to manage inflationary pressures while utilizing interest rate and exchange rate policies
strategically to stimulate economic growth.

Convergence of Implicit Noor Iteration in Convex b-Metric Space

G. Akinbo — 2025-03-20

The convergence to a fixed point and stability of the implicit Noor iteration in a convex b-metric
space is established in this work. The class of mappings considered here is an extension of a
class of weak contractions which has been used by several authors to obtain quite interesting
results on the existence of unique fixed points as well as convergence and stability of iterative
schemes in the literature.

Schwartz Space and Radial Distribution on the Euclidean Motion Group

U. E. Edeke — 2025-04-10

Let G = R2 ⋊T be the Euclidean motion group and let K(λ, t) = I0(λ)δ(t) be a distribution on G, where I0(λ) is the Bessel function of order zero and δ(t) is the Dirac measure on SO(2) ∼ = T, the circle group. In this work, it is proved, among other things, that the distribution K(λ, t) is tempered, positive definite, bounded and radial. Further more, a description of temperature function on G ,realised as the positive definite solution of the Laplace-Beltrami operator on SE(2), is presented

Perfect Product of two Squares in Finite Full Transformation Semigroup

A.T Imam — 2025-04-10

In this paper, we investigate the concept of the perfect product of two squares in the context
of finite full transformation semigroups. We provide a comprehensive analysis of the conditions
under which the product of two idempotent elements in a transformation semigroup forms a
perfect product of two squares. Specifically, we examine the relationship between the kernel
and image of idempotents, as well as the interplay between the domain and image of these
transformations. The main result establishes that for two idempotent elements α and β in Tn,
if the domain and image of α and β satisfy certain equivalence conditions, then their product is
a perfect product of two squares. We also explore related properties of disjoint cycles and how
these contribute to the structural characteristics of the semigroup. Our findings extend the
existing theory of transformation semigroups and offer valuable insights into the decomposition
of semigroup elements into squares, contributing to the broader field of semigroup theory.