Earthline Journal of Mathematical Sciences

Some New Classes of General Harmonic-like Variational Inequalities

Muhammad Aslam Noor — 2025-09-08

Several new classes of general harmonic-like variational inequalities involving two arbitrary operators are introduced and considered in this paper. Some important cases are discussed, which can be obtained by choosing suitable and appropriate choice of the operators. Projection technique is applied to establish the equivalence between the general harmonic-like variational inequalities and fixed point problems. This alternative formulation is used to discuss the uniqueness of the solution as well as to propose a wide class of proximal point algorithms. Convergence criteria of the proposed methods is considered. Asymptotic stability of the solution is studied using the first order dynamical system associated with variational inequalities. Second order dynamical systems associated with general quasi variational inequalities are applied to suggest some inertial type methods. Some special cases are discussed as applications of the main results. We also show that the change of variable can be used to show that the harmonic-like variational inequalities. Several open problems are indicated for future research work.

Stochastic Dynamics of Dual-Prey–Predator Interactions under Harvesting Pressure: Insights from the California Current Ecosystem

Chandrima Talapatra — 2025-09-09

This study presents a stochastic predator-prey model involving two harvested prey species—sardines and anchovies—and a common predator, the blacktip shark, under the influence of environmental noise. The model incorporates Holling type-II functional responses, harvesting efforts, and white noise perturbations representing environmental variability. Analytical investigations determine the boundedness and stability conditions of equilibria. Numerical simulations reveal that the predator population is highly sensitive to stochastic perturbations, particularly the noise intensity associated with predator mortality. Notably, a sufficiently large noise intensity in anchovy dynamics ($\alpha_2 > 72.06$) can stabilize the coexistence equilibrium, where higher values of $\alpha_1$ and $\alpha_2$ tend to destabilize the system. Phase portraits and bifurcation analyses illustrate the effects of harvesting rates and noise intensities on species persistence and extinction. These findings highlight critical thresholds for sustainable harvesting and noise tolerance, offering ecological insights into species coexistence within the California Current ecosystem.

Threshold Selection for Peak Over Threshold Models Using Logistic Regression

Temitope Comfort Iroko — 2025-09-11

Threshold selection remains a critical challenge in the application of Extreme Value Theory (EVT), particularly in actuarial science, where accurate modeling of extreme insurance claims is vital for solvency, capital adequacy, and reinsurance pricing. Traditional graphical tools, such as the mean residual life (MRL) plot, are highly dependent on visual interpretation and expert judgment, which limits reproducibility and consistency between practitioners. This paper proposes a machine learning approach using logistic regression to assign extremeness probabilities to insurance claims. The model is trained on labels generated from an initial quantile-based rule, classifying claims above the 90th percentile as extreme. The optimal threshold is determined as the smallest amount of claim with predicted probability exceeding a predefined cut-off (e.g., $90\%$). This probability-based rule provides an objective alternative to visual diagnostics and aligns well with classical EVT tools such as the MRL plot. After identifying exceedances above the selected threshold, a Generalized Pareto Distribution (GPD) is fitted using maximum likelihood estimation. Tail-based risk measures, including Value at Risk (VaR) and Expected Shortfall (ES), are then computed at the $99\%$ confidence interval to quantify the severity of potential extreme losses. The proposed framework is interpretable, reproducible, and readily applicable in actuarial workflows, offering a more consistent and automated solution for tail risk modeling.

Common Fixed Point Theorem for Berinde Weak Type Contraction Via Interpolation

Clement Boateng Ampadu — 2025-09-14

In this paper, we introduce the notion of an interpolative Berinde weak pair contraction, and obtain a common fixed point theorem in the setting of metric spaces. We illustrate the main result of the paper with an example.

Examining New Convex Integral Inequalities

Christophe Chesneau — 2025-09-14

In this article, we introduce new convex integral inequalities based on a contemporary and adaptable analytical framework. These inequalities can handle composed functions, integral expressions, and ratio-type functionals, which make them applicable to a wide range of analysis problems. Our main result, in particular, complements a recent theorem from the literature by providing a valuable and non-trivial lower bound. The proofs are presented in full detail to ensure mathematical rigor, clarity, and reproducibility.

Properties of Generalized Strongly Close-to-convex Functions

Khalida Inayat Noor — 2025-09-15

This paper defines certain subclasses of analytic functions and various properties including necessary conditions, distortion result, inclusion properties are investigated. In addition radius problems are discussed. Several known consequences of our investigations are also pointed out.

Single and Multivalued Extended Interpolative Berinde Weak Type F-Contraction Mapping Theorem

Clement Boateng Ampadu — 2025-09-15

In this paper we introduce the notion of an extended interpolative single and multivalued Berinde weak type F-contraction, and obtain some fixed point theorems for such mappings. An example is given to illustrate the main result.

On New General Beesack-Opial-type Integral Inequalities

Christophe Chesneau — 2025-09-22

This article presents new Beesack-Opial-type integral inequalities incorporating three functions. The upper bounds are defined using some derivatives and primitives of these functions. Detailed proofs are provided. These are accompanied by illustrative examples, including applications involving the Laplace transform.

On a New Integral Inequality Derived from the Hardy-Hilbert Integral Inequality

Christophe Chesneau — 2025-09-22

This article is devoted to a new integral inequality expressed in terms of elementary integrals. The proof is notable for its use of the classical Hardy-Hilbert integral inequality, which provides an elegant and concise argument. As an illustration of its utility, we also present an application to the gamma function.