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

2025-01-10T16:42:35+00:00

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

2025-03-07T10:29:34+00:00

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

2025-01-09T09:58:42+00:00

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

2024-06-21T19:39:36+00:00

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

2024-12-26T19:53:31+00:00

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

2024-10-06T03:12:01+00:00

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

2024-10-31T14:15:47+00:00

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

2025-06-15T16:52:00+00:00

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

2025-05-22T08:51:32+00:00

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

2025-06-10T08:35:09+00:00

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.

The Development Criterion for Exponential Function Projective Synchronization and Guaranteed Cost Controller of Complex Dynamical Networks Utilizing Multi-Connections and Time-Varying Delays

2025-04-22T05:36:11+00:00

This paper addresses cost-constrained synchronization control in complex dynamical networks (CDNs) with mixed time-varying delays, asymmetric couplings, and multi-connections. A novel criterion for exponential projective synchronization and guaranteed-cost control is developed using the Lyapunov–Krasovskii functional method, extended reciprocally convex and free-matrix-based inequalities, and LMIs. The proposed scheme reduces the cost upper bound via a new quadratic cost function. A numerical example illustrates the effectiveness of the approach.

Semi-Analytic Solution of Fractional Fokker-Planck and Fornburg-Whitham Equations Using a Unique Technique

2025-06-12T08:29:40+00:00

In this work, a new hybrid semi-analytical method is presented, merging the Kamal Transform and the Homotopy Perturbation Method (HPM), for solving fractional differential equations (FDEs) involving the Caputo derivative. The method is used to solve complex systems such as the Fokker-Planck and Fornberg-Whitham equations. This method beats classical iterative techniques in both computational efforts and simplicity. Numerous tables and graphics display the numerical results, establishing the method's accuracy by reference to the residual power series method and exact solutions. Our results illustrate the strength and the precision of this technique to be very efficient with a minor cost against numerical solution techniques for fractional partial differential equations.

Fixed Point Theorems in the Fuzzy Supermetric Spaces and Application

2025-06-25T17:12:03+00:00

This article introduces a new mathematical concept that extends the notion of a supermetric space, termed a fuzzy supermetric space. An illustrative example is provided to validate the proposed concept, and a class of contractive mappings is developed and employed to establish the existence and uniqueness of fixed-point theorems within the framework of fuzzy supermetric spaces. These results generalize both classical and recent findings as special cases within a broader, more inclusive setting, offering a more suitable framework for modeling and solving real-world problems. In addition, the concept of \((\beta{-}\theta)\)-contractive mappings is examined in this context. Finally, the theoretical results are applied to demonstrate the existence of a solution to the Fredholm integral equation.

Common Interpolative Rational Type Contractions in Bipolar Metric Spaces

2025-06-13T17:41:46+00:00

The main objective of this study is to introduce an extended class of interpolative rational contractions in bipolar metric spaces and to establish common fixed point theorems for such mappings. Specifically, we consider mappings that satisfy a general contractive condition involving multiple distance terms and an associated control function, broadening the existing framework of fixed point theory. Our results not only unify but also significantly improve upon several well-known fixed point theorems in the current literature, including classical results for single mappings as well as those for pairs of mappings.

Moreover, the common fixed point results presented in this work are particularly noteworthy because they apply to pairs of mappings that share a common fixed point, even in the absence of strict monotonicity or continuity assumptions usually required in traditional fixed point theorems. This enhancement broadens the scope of applications to a wider range of problems in nonlinear analysis and optimization.

To demonstrate the practical relevance and sharpness of our theoretical findings, we also provide illustrative examples. These examples highlight how the newly established theorems can be applied in various mathematical settings, showcasing their robustness and versatility.

Stability and Convergence Theorems for Enriched Kannan Mappings in \(\operatorname {CAT_p}(0)\) Spaces with Aplications

2025-07-11T02:26:11+00:00

This paper establishes convergence results for enriched Kannan mappings in \( \operatorname{CAT_p}(0) \) spaces, emphasizing both \( \Delta \)-convergence and strong convergence of CR-type iterative schemes. A Krasnoselskii-type assignment is shown to meet the contractive criteria of classical Kannan mappings. Stability under perturbations is also analyzed. An application to the Split Feasibility Problem is presented, including a numerical example in image reconstruction. Additional numerical experiments illustrate the theoretical findings.

A Halpern Method for Solving Perturbed Double Inertial Krasnoselskii-Mann Iterations with Applications to Image Restoration Problems

2025-06-15T05:03:23+00:00

In this paper, we introduce and study a Halpern inertial method for solving the general perturbed Krasnoselskii-Mann type algorithm in Hilbert space settings, where the underlying mapping is quasi-nonexpansive. We discuss convergence analysis of the method under some mild assumptions on the control sequences. We additionally present a numerical example to demonstrate the effectiveness of the method. Finally, we apply the method in solving image restoration problems. We evaluate the quality of the improvement in the Signal-to-Noise Ratio (ISNR) and the restored images using the Structural Similarity Index Measure (SSIM) metrics. The results of this work generalize and expand upon numerous results found in the literature.

Improving the XRani Distribution's Inference: Applying Confidence Intervals to PM2.5 Concentration Data Collected in Bangkok, Thailand

2025-05-21T02:07:12+00:00

This paper developed and assessed four methods for constructing confidence intervals (CIs) for the parameter of the XRani distribution, which is frequently applied in the analysis of lifetime data. The CIs examined include the likelihood-based CI, Wald-type CI, bootstrap-t CI, and the bias-corrected and accelerated (BCa) bootstrap CI. To evaluate their performance, both a simulation study and a real-world application were conducted. The evaluation criteria focused on empirical coverage probability (ECP) and average width (AW) across a range of scenarios. To enhance computational efficiency, an explicit analytical expression for the Wald-type CI was derived. Simulation results demonstrated that the likelihood-based and Wald-type CIs consistently achieved ECPs close to the nominal 0.95 confidence level across most scenarios. In contrast, for smaller sample sizes, the bootstrap-t and BCa bootstrap methods yielded lower ECPs. However, as sample sizes increased, the ECPs of both bootstrap methods gradually approached the nominal level. The parameter values were also found to influence performance: at lower parameter values, all CIs performed well, with the likelihood based and Wald-type methods maintaining an ECP close to 0.95. At higher parameter values and smaller sample sizes, however, the bootstrap-t and BCa methods exhibited diminished coverage probabilities. The practical utility of these CI methods was further demonstrated through the applications to PM2.5 concentration data collected in Bangkok, Thailand. The results from this empirical analysis corroborated the findings of the simulation study, thereby affirming the robustness and applicability of the proposed CI methods.