Bangmod International Journal of Mathematical and Computational Science

The Hybrid Steepest Descent Method with Implicit Double Midpoint for Solving Variational Inequality over Triple Hierarchical Problems

Sangkhae Suwansoontorn — 2025-01-25

Because of the importance of the variational inequality problem that related to many other problems in various branches of science and engineering, it becomes one of the most popular topics which many researchers pay deeply attention to study on the way to solve and the way to apply. In this research, we study the monotone variational inequality over triple hierarchical problem. We propose a new implicit algorithm to find the solution with the strong convergence theorem which is proved and applied to guarantee its solution under some weak assumptions. Our results enhance those of Xu et al., Ke and Ma, Dhakal and Wutiphol and many other authors.

A Two-Step Inertial CQ Method for Split Feasibility Problems with Applications

Abubakar Adamu — 2025-03-07

This paper introduces an algorithm for approximating solutions of split feasibility problems by employing a two-step inertial acceleration strategy along with a self-adaptive step size. This combination enhances the convergence rate and reduces computational complexity of the proposed algorithm. The nonasymptotic O(1/t) convergence rate and global convergence of the proposed method are established within the context of Euclidean spaces. The algorithm is extended to handle multiple set split feasibility problems, and a sensitivity analysis is conducted to identify optimal inertial parameter choices. Additionally, the algorithm is applied to the LASSO problem. Comparative evaluations with various algorithms from existing literature showcase the superior performance of the proposed algorithm.

The Plethystic Exponentials Created in Certain Domains of the Complex Plane and Related Implications

H¨useyin Irmak — 2025-03-19

The primary aim of this scientific investigation is to introduce basic information about plethystic exponential forms, which play significant roles in both mathematics and related fields. It then aims to reorganize these concepts within specific regions of the complex plane, focus on new complex ideas, and present various propositions, along with their implications and potential applications, for consideration by relevant researchers.

Guaranteed Pursuit Time for an Inﬁnite System in \(l_2\) with Geometric Constraints

Bashir Mai Umar — 2025-04-06

In this paper, we consider a pursuit differential game problem described by an infinite system of binary differential equations in the Hilbert space \(l_2\). The control parameters of the players are subject to geometric constraints. The pursuer's goal is to complete the game by bringing the state of the system to the origin, while the evader's goal is the contrary. The guaranteed pursuit time required to achieve the pursuer's goal is estimated. To this end, we constructed
an optimal strategy for the pursuer.

Controlling the Spread of Malaria-Cholera Co-infection with Effective Intervention Strategy

Abdulfatai Atte Momoh — 2025-04-25

This paper proposes an optimal control of intervention strategies for malaria-cholera co-infection with emphasis on five control strategies namely: treated bed nets, treatments of malaria, indoor residual spray, sanitation and treatment of cholera to prevent disease spread in a population. A non-linear system of differential equations is formulated to study the dynamics of the proposed model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) states were obtained. The basic reproduction numbers, \(\mathcal{R}_0^{C},\,\mathcal{R}_0^{V}\) that determine the transmission of the diseases were derived. A sensitivity analysis on the reproduction numbers to determine the parameters that have impact on the reproduction number were carried out. Using the Routh-Hurwitz criterion and Castillo-Chavez techniques, the conditions for stability of the disease-free equilibrium were established. The result of the stability revealed that, if the reproduction number is kept below to unity, malaria-cholera co-infection can be entirely eradicated. The sensitivity analysis results paved way for the implementation of a controlled system, which was solved using Pontryagin's Maximum Principle (PMP) and an optimality system was obtained. The optimality system was then solved numerically using forward backward sweep approach and graphs were produced.

Strong Convergence Accelerated Alternated Inertial Relaxed Algorithm for Split Feasibilities with Applications in Breast Cancer Detection

Abdulwahab Ahmad — 2025-04-30

In this article, we construct an accelerated relaxed algorithm with an alternating inertial extrapolation step. The proposed algorithm uses a three-term conjugate gradient-like direction, which helps to fasten the sequence of its iterates to a point in a solution set. The algorithm employs a self-adaptive step-length criterion that does not require any information related to the norm of the operator or the use of a line-search procedure. Moreover, we formulate and prove a strong convergence theorem for the algorithm to a minimum-norm solution of a split feasibility problem in infinite-dimensional real Hilbert spaces. Furthermore, we investigate its applications in breast cancer detection by solving classification problems for an interesting real-world breast cancer dataset, based on the extreme learning machine (ELM) with the \(\ell_{1}\)-regularization approach (i.e., the Lasso model) and the \(\ell_{1}\)-\(\ell_{2}\) hybrid regularization technique. The performance results of the experiments demonstrate that the proposed algorithm is robust, efficient, and achieves better generalization performance and stability than some existing algorithms in the literature.

Accessing the Thermodynamics of Ferromagnetic Sutterby Nanofluid with Effect of Homogeneous-Heterogeneous and Chemical Reactions

Auwalu Usman — 2025-05-26

The effect of magnetic dipole, pourosity parameters, and heat transfer on the flow of ferromagnetic Sutterby nanofluid on a curved stretching sheet is investigated in this paper. The effect of gyrotactic microorganisms and the homogeneous-heterogeneous reaction model are also taken into account. The momentum, energy, and gyrotactic microorganisms equations, together with the interaction of ferromagnetic particles, form the problem's governing equations, which are then transformed into non-linear ordinary differential equations via similarity transformations and solved using an efficient and strong homotopy analysis method. The effects of parameters under the consideration of dimensionless velocity, temperature, homogeneous-heterogeneous concentration, and motile microorganisms are graphically depicted. The magnetic dipole effect and thermal radiation parameter improved the temperature. The homogeneous-heterogeneous concentration declined as the homogeneous chemical reactions parameter increases and the motile density of microorganisms decreases as the Lewis number increases. The result agreed with many published results as expected.

Elegant Rational Contractive Conditions with Applications to Implicit Functional Integral Equations

Syed Irtaza Hassnain — 2025-06-26

This paper aims to introduce several new classes of contraction mappings inspired by convex and rational contraction mappings. We establish the existence and uniqueness of fixed points for each newly proposed contraction mapping in metric spaces. To validate our theoretical findings, we provide several illustrative examples that demonstrate cases where well-known fixed point results, such as the Banach contraction principle, the Kannan fixed point theorem, the Chatterjea fixed point theorem, the Jaggi fixed point theorem, and the Istratescu fixed point theorem, are not applicable. As an application, we employ our theoretical fixed point results to investigate the existence and uniqueness of solutions to nonlinear implicit integral equations.

Convergence Theorem of Inertial Projection and Contraction Methods for Pseudomonotone Variational Inequalities Problem

Anantachai Padcharoen — 2025-06-26

This paper presents a novel convergence theorem for an inertial projection and contraction-based method aimed at solving pseudomonotone variational inequality problems (VIP) in real Hilbert spaces. The proposed algorithm combines inertial dynamics and contraction projections to enhance the convergence speed and stability of solutions, even when the operator involved is not strongly monotone but pseudomonotone. We establish the strong convergence of the method under mild conditions, demonstrating its effectiveness in non-strongly monotone settings. The theoretical analysis is complemented by numerical experiments, which show that the proposed method significantly outperforms classical projection and extragradient methods in terms of both computational efficiency and iteration count. This work contributes to the broader field of nonlinear optimization by providing a robust and efficient solution approach for VIP with pseudomonotone operators, and it opens pathways for further research on adaptive and large-scale extensions of the method.

Induced Bilal Distribution: Statistical Properties with Applications to Model Precipitation and Vinyl Chloride Data

Chom Panta — 2025-06-26

This paper proposes a new one parameter life distribution called induced Bilal distribution for modeling some real data. The main mathematical characteristics of this distribution are derived and discussed including the cumulative distribution and probability density functions, the moments, coefficient of variation, skewness, kurtosis, mean and median deviations, Gini index, Lorenz curve, Bonferroni curve, Rényi entropy, stochastic ordering, and distribution of order statistics. Also, reliability analysis based on the odds function, survival function, reversed hazard rate function, hazard function, and the stress-strength reliability function are provided. Estimation of the model parameter is performed using the maximum likelihood method and a simulation study is supported to illustrate the estimator behaviors. Using two real data sets related to the precipitation in Minneapolis and vinyl chloride, it is shown that the new distribution outperforms some well-known important existing competitors considered in this study.