Open Journal of Mathematical Sciences (OMS)

Some new classes of inverse variational inequalities, which can be viewed as a novel important special case of general variational equalities, are investigated. Projection method, auxiliary principle and dynamical systems coupled with finite difference approach are used to suggest and analyzed a number of new and known numerical techniques for solving inverse variational inequalities. Convergence analysis of these methods is investigated under suitable conditions. One can obtain a number of new classes of inverse variational inequalities by interchanging the role of operators. Some important special cases are highlighted. Several open problems are suggested for future research.

We introduce the concept of projective suprametrics and provide new part suprametrics in a normed vector space ordered by a cone. We then examine how the convergence of the underlying norm relates to that of the projective and given suprametrics, and we establish sufficient conditions for the completeness of certain subsets. Moreover, we prove a version of Krein-Rutman theorem via a fixed point theorem in suprametric spaces, and study spectral properties of positive linear operators. Furthermore, we show that operator equations involving some concave or convex operators satisfy a Geraghty contraction and therefore have solutions. As an application, we prove a Perron-Frobenius theorem for a tensor eigenvalue problem.

We characterize the boundedness and compactness of generalized integration operators acting between Fock spaces and apply these characterizations to investigate the path-connected components and the singleton of path-connected components of the space of bounded generalized integration operators. Moreover, we describe the essential norm of these operators.

This article considers a second-order difference equation with constant coefficients in its standard form and two different classes of two-point homogeneous boundary conditions. First, we construct the corresponding Green functions and derive some important properties for further analysis. Next, we propose adequate conditions for the existence of solutions to the considered boundary value problems. Finally, we offer two examples to show the applicability of the main results.

In this paper, we establish several new arctangent- and logarithmic-Hardy-Hilbert integral inequalities. The approach combines fundamental principles with refined techniques from the theory of integral inequalities, leading to a range of original results. Complete proofs are presented together with a discussion of their sharpness and potential applications.

This note introduces a \(1\)-parameter of cubic curves naturally associated to the sphere \(S^4\) considered in the unique \(5\)-dimensional irreducible representation space of \(SO(3)\). Eight examples are discussed with the last two being elliptic curves. Also, two conics are defined naturally in our setting by a special basis of the Lie algebra \(sl(3, \mathbb{R})\).

This paper introduces a unified framework for fixed point theorems involving asymptotically regular mappings in \(b\)-metric spaces through the concept of contractive families. We establish a general fixed point theorem that encompasses various existing results, including those of Kannan-type and generalized contractive conditions, as special cases. In particular, we demonstrate that the recent results of Nagac and Tas [1] emerge naturally as special cases of our main theorem through appropriate parameter choices. The main result employs coefficient functions and a general auxiliary function with strengthened continuity conditions, providing flexibility that allows the derivation of numerous particular cases. Several corollaries with complete proofs are presented to demonstrate that our results properly generalize and extend well-known theorems in the literature.

This paper presents a thorough investigation of Laplace transforms for a wide range of probability distributions, including both classical and generalized forms. Analytical derivations are complemented with extensive numerical examples and graphical simulations to validate the theoretical results. Applications in reliability theory and system availability are discussed, highlighting the practical significance of the findings for modeling and performance evaluation of complex systems.

Pre-exposure prophylaxis (PrEP) is an effective strategy for HIV prevention, offering individual protection and broader public health benefits. Enrollment in PrEP programs not only provides access to HIV prevention but also serves as a strategic entry point for the diagnosis of other sexually transmitted infections (STIs). Because participation requires regular HIV testing and routine STI screening (e.g., for syphilis), PrEP implementation facilitates early detection and treatment of coexisting infections, strengthening integrated sexual health surveillance and control efforts. We developed a mathematical model capturing syphilis dynamics, incorporating PrEP as a mechanism for diagnosis and treatment engagement. The model considers coinfection via high-risk sexual contact, partial protection of PrEP (HIV but not syphilis), and diagnostic pathways linked to PrEP program entry. Independent analysis of syphilis (without PrEP) established population persistence, basic reproduction numbers, and stability of disease-free and endemic equilibria. Integrating PrEP, we derived conditions under which PrEP-related parameters—particularly diagnostic access—positively influence syphilis transmission dynamics. Sensitivity analysis showed that higher PrEP adherence reduces reproduction numbers for syphilis and coinfection. Computational simulations using literature-based parameters confirmed these findings: increased PrEP use and lower discontinuation rates decreased new infections and improved treatment outcomes. These results highlight the role of PrEP in improving the detection and treatment of syphilis and HIV–syphilis coinfection.

In recent decades, a wide range of Hardy-Hilbert-type integral inequalities have been established. This article focuses on a one-parameter result introduced by Waadallah Tawfeeq Sulaiman in 2010, which has a unique structure: the double integral involves a power-sum of the variables, as well as a technical power-minimum. The sharp constant factor is also elegantly expressed in terms of the beta function. However, the parameter involved is subject to restrictions on its values. In this article, we refine the inequality by removing this restriction and addressing a theoretical gap in the original proof to yield a sharper result. We provide a thorough, step-by-step proof and demonstrate how this new result can be used to derive additional variants and extensions.