European Journal of Mathematical Analysis

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.