European Journal of Mathematical Analysis

A Population Model with Smooth Functions and Application

2026-01-20T08:57:45+08:00

The purpose of this paper is to give sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain \(\Omega\) in \(R^{n}\). Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive coexistence of species of animals with predator-prey relation in many biological models.

Safety Critical Thresholds and Stability Analysis of Collective Cooperation with Heterogeneous Contributions

2026-04-09T00:07:14+08:00

This paper addresses the problem of individual defection (voluntary exit) in collective cooperation. Based on an upper-bounded S-shaped contribution-payoff function, we construct a Homogeneous Equal-Contribution Model and a One-Strong-n-Weak Heterogeneous Model with a high-contribution agent. We strictly define and derive three core safety critical thresholds for collective cooperation: the failure threshold of equal allocation, the failure threshold of proportional allocation, and the full stability threshold. Through rigorous algebraic derivation and functional property analysis, we provide explicit closed-form solutions and solving methods for all thresholds, prove the self-consistency of the model, and reveal the mechanisms by which individual heterogeneity, group size, contribution intensity, and task attributes affect the stability of collective cooperation. This paper provides a complete and unified mathematical theoretical framework for the stability analysis of collective cooperation.

Generalized Trapezium-Type Inequalities via Modified (h,m)-Convex Functions of the Second Type

2026-06-03T08:29:51+08:00

In this article, we establish a generalized framework for integral inequalities by introducing an integral family of trapezoidal fractional estimates. Using a generalized weight function ϖ′(τ), we prove a new integral identity that establishes clear relationships between general fractional operators and differentiable functions. Using this result together with the classical Hölder, Power Mean, and Young inequalities, we derive several precise upper bounds for the trapezoidal remainder by assuming that the absolute value of the first derivative belongs to the class of modified convex (h,m)-functions of the second type. Throughout the work, we show that several seminal results reported in the literature are special cases of our own. Finally, we provide concrete applications to precise error estimates for special means.

Non-Autonomous Cantor Sets from Decimal Expansions

2026-05-06T00:50:32+08:00

We construct irregular Cantor sets C_ξ ⊂ [0,1] using the decimal digits of a real number ξ (typically transcendental) as level-dependent removal ratios. Under the mild assumption that only finitely many digits are zero (satisfied, for example, by ξ = π − 3 and ξ = e − 2 after discarding finitely many initial digits), the resulting sets are compact, perfect, totally disconnected, and nowhere dense. The natural probability measure μ_ξ splits mass equally at each construction step. We prove that the Hausdorff dimension is given by dim_H C_ξ = lim inf_k→∞ log 2 / (−(1/k) ∑_j=1^k log a_j) where a_k = ½(1 − d_k/10), and that the associated Cantor function F_ξ(x) = μ_ξ([0,x]) is Hölder continuous with optimal exponent equal to this dimension. The construction extends to Cartesian products K_n = C_ξ₁ × ⋯ × C_{ξ_n}; the Hausdorff dimension adds, and the product Cantor function F_n(x₁,…,x_n) = ∏_i F_{ξ_i}(x_i) is Hölder continuous with exponent min_i dim_H C_{ξ_i}. Connections to normal numbers (which yield dimension ≈ 0.874) and Liouville numbers (which can realise any dimension in (0,1]) are discussed, and several open problems are formulated.

Orthogonal F-Quasi-Contractions on O-Complete Metric Spaces with Applications

2026-03-24T17:07:57+08:00

In this paper, we introduce the notion of orthogonal F-quasi-contractions on orthogonal metric spaces. We establish two fixed point theorems for such mappings: one requiring orthogonal continuity and another in which this assumption is relaxed. When the orthogonality relation is taken to be universal, the results yield new fixed point theorems for F-quasi-contractions on complete metric spaces. We construct examples to show that the newly introduced notion overlaps with and extends the F-weak contractions and F-contractions notions to handle more complex, non-continuous, or asymmetrical mapping behaviors.

As an application, we prove the existence and uniqueness of a solution to an initial value problem for a general Volterra-type integro-differential equation. Such equations arise in various fields, including epidemic modeling, control theory, and physics.

A Two-Step Conformable Fractional Iterative Method with Stability and Applications to Nonlinear Problems

2026-04-19T17:28:02+08:00

In this paper, a two-step iterative method based on conformable fractional derivatives is proposed for solving nonlinear equations. The convergence analysis confirms that the method achieves fourth-order convergence. Numerical experiments on real-world problems reveal that the method significantly reduces the number of iterations compared to classical schemes. The method is also tested on several important models, including the Van der Waals equation, blood flow dynamics, population growth laws, chemical engineering models, and Planck's radiation law, demonstrating its wide applicability. Furthermore, the basin of attraction analysis shows improved stability and efficiency, highlighting the method's potential as a reliable alternative for nonlinear problem-solving.

Boas-Type Theorems for the Mehler-Fock-Clifford Transform

2026-03-29T06:17:24+08:00

In this paper, we give necessary and sufficient conditions in terms of M(f), the Mehler-Fock-Clifford transform of f, to ensure that f belongs either to one of the generalized Lipschitz classes H_α^m and h_α^m for α > 0.

Generalized Beta Distribution: Theoretical Properties and Applications in Health Data Modeling

2026-03-02T00:58:14+08:00

In this publication, a generalization of the classical Beta distribution by five parameters, called the Generalized Beta (GB) distribution, is introduced and well examined, particularly on the usage of the health data. The GB distribution provides the highest flexibility ever in the modeling of complex data patterns in med and public health analyses including the incidence of illnesses, response to treatments, and the values of biomarkers. Systematically basic statistical properties, including correct formulations of moments, moment-generating functions, characteristic functions, hazard functions, and entropy measures, are obtained in this paper. The article gives novel recurrence relations of moments and incomplete moments, which are computationally useful in their application. The paper delves deep into correlation with other important statistical distributions like Kumaraswamy, generalized Gamma, Power Function and Mc-Donalds generalized distributions, by in-exhaustive mathematical analysis. This paper constructs robust parameter estimations practices on both frequentist (maximum likelihood), and in the Bayesian paradigm which have been examined in long simulating studies of parameter regimes, and sample sizes. The practical usefulness of the distribution could be demonstrated by the extensive simulation experiments re-creating the real world conditions of health data, including the disease prevalence modeling, the efficacy of disease treatments analysis, biomarker analysis. GB distribution has excellent flexibility to observe distributional properties of complexity like multimodality, heavy tails and fine skewness patterns which are often nonparametrically challenging in current statistical models applied in health research. Extensive goodness-of-fit statistics, model comparison conditions and diagnostic tests are used to establish the improved performance of the distribution compared to the available options.

Mathematical Analysis of Corruption Dynamics Incorporating the Corrupt Individuals Under Investigation Class and Recidivism

2026-06-25T04:16:22+08:00

Corruption is a complicated social, political, and economic phenomenon that impacts both public and private officials, as well as the nation as a whole. Several studies have likened it to an harrowing contagious disease because of its propensity to proliferate in the society by replicating itself from one individual to another and it causes debilitating effects to a country's economy. Despite the fact that many nations employ a variety of strategies to curb the spread of corruption, the vice incessantly persists. To ascertain the impact of control measures on corruption's propagation, a nonlinear deterministic mathematical model that describes its dynamics is developed and analyzed in this study. The study incorporates rigorous analysis to verify the existence, positivity, and boundedness of the solution, as well as the stability of the equilibrium points. It is confirmed that whenever the corruption reproduction number R₀ is less than one, the corruption-free equilibrium (CFE) is globally asymptotically stable. Using the normalized forward sensitivity approach, we determined the prerequisite for the optimal approach to mitigate the propagation of corruption. It is evident that 10% increase in corruption initiation rate β causes a corresponding 10% increase in R₀, while 10% increase in efficacy of anti-corruption and religious instructions ψ as well as incarceration rate γ₃ causes a reduction of R₀ by 6.462% and 1.686% respectively. On the numerical segment, python software was utilized to illustrate the time series solution. The numerical findings were in concurrence with the analytical results. This study recommends a tripartite approach to eradicating corruption over time. This involves effective anti-graft campaigns and religious teaching, establishment of an efficient and robust whistle-blowing protocols and lastly the imprisonment of individuals found culpable of committing corruption regardless of their socio-economic statuses.

On Two One-Parameter Variants of the Hardy-Hilbert Integral Inequality

2026-04-20T23:45:11+08:00

This article establishes two new one-parameter variants of the Hardy-Hilbert integral inequality. These results are derived by modifying an existing framework that incorporates the absolute difference between unity and the product of two variables, raised to an adjustable power parameter. By employing two distinct approaches, we obtain different weighted integral norms for the primary functions. The proofs are presented in comprehensive detail and are entirely self-contained.

Extended Gauss-Newton Method on Riemannian Manifolds for Convex Composite Optimization Problems

2025-11-25T11:16:52+08:00

The Gauss-Newton method has been used to generate a sequence to approximate a zero of a vector field defined on a Riemannian manifold. The sufficient convergence conditions are based on L-average continuity conditions on the covariant derivative. In this work, the convergence conditions are weakened with advantages: tighter error distances and more precise information about the zero. These improvements are realized since tighter majorizing sequences are generated than in earlier studies. The scalar functions controlling the derivative are at least as tight as the specializations of earlier ones. Therefore, the new results are obtained without additional computational effort. Numerical applications are utilized to verify the convergence conditions.

Inverse Sturm-Liouville Problems on Bounded Time Scales

2025-09-24T20:50:23+08:00

In this study, we introduce some properties of the Sturm-Liouville boundary value problem on bounded time scales. Then, to give the solution of inverse problems, uniqueness theorems are provided for two characteristic data: the Weyl function and a set of j-th eigenvalues of countably infinite Sturm-Liouville boundary value problems that are obtained by changing boundary conditions.

The Logistic-Gompertz-Law Distribution: A Statistical Framework for Modeling Legal Case Durations and Judicial Process Efficiency in Contemporary African Judiciary Systems

2025-11-03T08:55:31+08:00

This extensive study presents the new four-parameter probability distribution Logistic-Gompertz-Law (LGL) which is an original distribution that is designed to deal with the intricate time-dependence nature of the legal process in modern situations of the African courts system. Based on the classical Gompertz and Logistic distributions, the LGL distribution, a hybrid of sigmoidal growth dynamics and flexible hazard functions, will provide a potent statistical approach to the modeling of the legal case duration, the probability of a settlement, as well as the judicial efficiency metrics in various jurisdictional settings. We offer derivations of its statistical properties, such as closed-form expressions of probability density and cumulative distribution functions, hazard rates, and moment properties which have been proved up by long analytical methods. With extensive Monte Carlo simulations of three different legal cases that are common in African courts, that is, efficient, complex, and standard case proceedings, we reveal that the distribution performs well in terms of exhibiting the traditional S-curve trend of legal cases long observed by legal practitioners but previously immeasurable. Estimation procedures based on both maximum likelihood and Bayesian models are derived and proven. In goodness-of-fit, the LGL distribution always outweighs the traditional ones (Weibull, Gamma, Log-Normal), with the KS value of 0.1901 to 0.3263 and correlation coefficients greater than 0.95 in all cases, and indicating its greater applicability to the law-related temporal data. Applications to field Practical uses in case duration prediction, judicial efficiency measures, and legal resources optimization in the African judicial setting are well elaborated making the LGL distribution a significant legal analytics, court management and evidence-based judicial policy development tool in the developing judicial environment.

Growth of Solutions of Certain Linear Differential Equations With Dominant Coefficient of Lower [p, q]−Order Near a Singular Point

2025-09-21T22:53:06+08:00

In this article, we study the growth of solutions to certain linear differential equations with analytic coefficients in C − {z₀}, where z₀ ∈ C is an essential singularity. We derive estimates for the lower bounds of the [p, q]-order of these solutions. Our results improve and extend the previous findings of Liu, Long and Zeng, and those of Long and Zeng.

C-Class Functions and Fixed Points of Weakly Contractive Mappings in Rectangular b-Metric Spaces

2025-08-19T09:26:05+08:00

In this paper, we introduce C class-F-generalized weakly contractive mapping and prove the existence and uniqueness of fixed points of such maps in the setting of rectangular b-metric spaces. We provide an example in support of our result.

Schwarz Boundary Value Problem for Higher-Order Complex Partial Differential Equations on a Triangle

2025-11-20T21:37:24+08:00

In this paper, we consider the Schwarz boundary value problem for higher-order complex partial differential equations on a triangle. We first introduce the poly-Schwarz operator and the T-type operator for the triangle, and then investigate the boundary behavior of these operators. In addition, we discuss the solvability conditions and present an explicit solution to the Schwarz problem for the inhomoheneous polyanalytic equation on the triangle.

Groupoid Characterization of Partial Algebras on Sobolev Spaces

2025-12-19T06:25:16+08:00

The \(L^p\)-spaces, with \(p \not = \infty\), form a partial algebra \((L^p(\Omega), \Gamma, \cdot)\) with pointwise multiplication of functions. The Sobolev spaces \(W^{k,p}(\Omega)\), delineated by weak derivatives as subspaces of \(L^p\)-spaces is shown to contain the partial algebra \((L^p(\Omega), \Gamma, \cdot)\) generalized by the partial action of the smooth algebra \(\mathscr{K}(\Omega)\) by convolution on the Banach spaces \(L^p(\Omega)\). We characterised the Sobolev space \(W^{k,p}(\Omega)\), invariant under \(\mathscr{K}(\Omega)\) partial action, using Lie groupoid framework, and study the partial algebra as defining the partial dynamical systems on the \(L^p\)-space associated with the weak differential operators. The locally convex partial \(^*\)-algebra \((L^p(\Omega), \Gamma, \cdot,^*)\) defines the stable local flows coinciding with local bisections of the Lie groupoid. The unitary representation of resulting Lie groupoid \(\mathscr{W} \rightrightarrows W^{k,p}(\Omega)\) on the associated Hilbert bundle demonstrates the simplification achieved by the characterisation.

Donoho-Stark Theorem for the Second Hankel-Clifford Transform

2025-10-26T06:08:11+08:00

In this work, we obtain an analog of Donoho-Stark theorem for the second Hankel-Clifford transform for functions in \(f \in L^1_{\mu} \cap L^2_{\mu}\), using the properties of this transform.

Multivalued Contractive-Type Extensions with Stability and Well-Posedness in Cone b-Metric Spaces under (λ, s)-Convexity and Applications

2025-08-28T19:30:49+08:00

We introduce new extensions of multivalued contractive fixed point results in complete cone b-metric spaces endowed with a normal cone structure. By developing a λ-iterative scheme combined with an approximate Hausdorff selection technique, we establish original Nadler-type and Berinde-type results with explicit convergence estimates depending on the b-metric coefficient s and the iteration parameter λ.
In addition, we prove a Berinde-type fixed point theorem for weak multivalued contractions, together with stability and well-posedness results under the sharp condition sδ < 1. The stability theorem provides quantitative bounds for perturbations of contractive multivalued operators, while the well-posedness result guarantees convergence of approximate solutions to the unique fixed point.
Applications to vector optimization and Nash-type equilibrium problems are presented within the framework of (λ, s)-convexity. The results extend classical fixed point theorems of Nadler and Berinde to the ordered and relaxed triangle inequality setting of cone b-metric spaces.

New Fixed Point Results for (τ -k)-F-Contraction Mappings in Complete Metric Spaces

2025-12-01T00:46:40+08:00

In this paper, we introduce and study two novel classes of contractions in complete metric spaces, namely the (τ , k)-F-contractions and (τ , k)-F-weak contractions. These notions generalize and unify several well-known contraction conditions in the existing literature. We establish sufficient conditions ensuring the existence and uniqueness of fixed points for such mappings in complete metric spaces. In addition, illustrative examples are presented to verify the applicability and effectiveness of the proposed results. The findings of this work extend and enhance many classical fixed point theorems within the framework of metric spaces.