Tamkang Journal of Mathematics

Existence of solutions to nonlocal weighted Kirchhoff-type problems via topological degree theory

Nezha KAMALI — Wed, 20 May 2026 00:00:00 +0000

This paper investigates a weighted Kirchhoff-type equation driven by the fractional $p(x,\cdot)$-Laplacian operator. The proposed model captures both nonlocal interactions and variable exponent effects, which naturally arise in several applied contexts. Under suitable structural assumptions, we analyze the associated nonlocal boundary value problem with Dirichlet conditions. By employing topological degree methods, we prove the existence of weak solutions, thereby extending and enriching existing results on Kirchhoff-type problems involving fractional and variable exponent operators.

On damping a delay control system with global contraction on a temporal tree

Alexsandr Lednov — Wed, 20 May 2026 00:00:00 +0000

We consider the problem of damping a control system with delay described by first-order functional-differential equations on a temporal tree. The delay in the system is time-proportional and propagates through the internal vertices. The problem of minimizing the energy functional with account of the probabilities of the scenarios corresponding to different edges is studied. We establish the equivalence of this variational problem to a certain boundary value problem for second-order functional-differential equations on the tree, possessing both the global contractions and the global extensions, and prove the unique solvability of both problems. In particular, it is established that the optimal trajectory obeys Kirchhoff-type conditions at the internal vertices.

A log-convex generalization of Alzer–Fonseca–Kovačec type inequalities and applications

Đặng Võ Phúc — Wed, 20 May 2026 00:00:00 +0000

We develop a multiplicative/logarithmic counterpart of the convexanalytic scheme of Phung–Huy [9] for Alzer–Fonseca–Kovačec type inequalities. At the scalar level, we establish comparison inequalities for strictly increasing log-convex functions on the logarithmic scale. We also record a derivative-weighted estimate expressed via the logarithmic derivative $r = (\log \varphi)'$, and we clarify parameter regimes where this derivative factor can improve the universal constant. Concrete applications are presented for the function $t^t$ and the Gamma function $\Gamma$. We then extend the scalar comparison to commuting positive definite matrices under unitarily invariant norms with the universal constant $\frac{v(1−v)}{\tau(1− \tau)}$. For the non-commuting case, we obtain “envelope” bounds via spectral pinching onto finite-dimensional abelian subalgebras, and we include a Heinz-centered quantitative estimate in the pinched abelian setting, combining a Lipschitz control for $g = \log \circ \varphi$ with the Heinz norm inequality under unitarily invariant norms.

Vanishing quasi-conformal curvature tensor of a certain class of almost contact metric manifolds

Farah Hasan AlHusseini, Habeeb M. Abood — Wed, 20 May 2026 00:00:00 +0000

This paper focuses on the essential role of the quasi-conformal curvature tensor in developing the theoretical foundation and applications of quasi-contact metric geometry. The quasi-conformal curvature tensor of NC$_{10}$-manifolds using the space associated with $G$ structures (AGS-space) has been investigated. By deriving explicit expressions for the tensor components, the necessary and sufficient conditions for considering the quasi-conformal NC$_{10}$-manifold as flat quasi-conformal have been determined. Noteworthy, it indicated that any flat quasi-conformal NC$_{10}$-manifold is locally isometric to the product of the Kähler manifold and the real line, thus connecting abstract tensor properties to classical geometric structures. Moreover, the conditions for the NC$_{10}$-manifold that yield the $\eta$-Einstein structure are established. New analogues of Gray’s identities for the quasi-conformal curvature tensor have been introduced for NC$_{10}$-manifold.

Multipliers of Bloch-Type and Zygmund-Type Spaces of Holomorphic Functions on the Unit Ball of $\Bbb{C}^n$

Lam Lien — Wed, 20 May 2026 00:00:00 +0000

The aim of this paper is to study the multipliers of Bloch-type and Zygmund-type spaces of holomorphic functions on the unit ball $\mathbb{B}_n \subset \mathbb{C}^n$. For the classical Bloch space, such multipliers were characterized by Zhu. Subsequently, Galindo and Lindstr"{o}m extended this investigation to the infinite-dimensional setting for the specific weight $\omega(z) = 1 - |z|^2$.

A model of HIV/AIDS transmission dynamics with treatment: The case of the DRC

Charles K. Mbayi, Jean-Marie N. Mpompi, Justin B. Munyakazi — Wed, 20 May 2026 00:00:00 +0000

In this paper, we propose a novel HIV/AIDS epidemic treatment model to reduce the number of HIV cases. We divide infected individuals into four compartments, that is, a compartment of infected individuals who are unaware of their HIV status and do not show any symptoms, a compartment of infected individuals who are aware of their status but do not show any symptoms, infected individuals in the asymptomatic compartment and a treatment compartment that receives infected individuals who are aware of their status, whether they are sick or not. The basic reproduction number $R_0$ for the proposed model is computed using the next generation matrix (NGM). Using a corollary of Gershgorin’s circle theorem, the results show that the disease-free equilibrium (DFE) is locally asymptotically stable (LAS) if $R_0 < 1$ and the endemic equilibrium (EE) is locally asymptotically stable if $R_0 > 1$. We also proved by means of the Lyapunov method that the disease-free equilibrium is globally asymptotically stable if $R_0 < 1$. Finally, numerical simulations of the model are conducted to support the theoretical results and also to investigate the sensitivity of certain parameters using HIV/AIDS data from the Democratic Republic of the Congo (DRC).